Forschung Harald Garcke

recent preprints:

• A unified energy-stable finite element approximation for evolving fluidic biomembranes (2026)
  (with Robert Nürnberg, Quan Zhao)

• Weak and strong solutions for a class of quasilinear Allen--Cahn systems (2026)
  (with Tim Laux, Andrea Poiatti)

• Analysis of a Cahn-Hilliard-Canham-Helfrich system for the evolution of a two-phase membrane (2026)
  (with Mathias Wilke)
   

• On a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities: Energy equality and Lyapunov stability (2026)
  (with Maoyin Lv, Hao Wu)

   

• On a Mullins-Sekerka model for the growth of active droplets modelling protocells: Stability analysis and numerical computations (2026)
  (with Kei Fong Lam, Robert Nürnberg, Andrea Signori)
  
   
• A parametric finite element approach for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling (2026)
  (with Tokuhiro Eto, Robert Nürnberg)
   
• An energy-stable minimal deformation rate scheme for mean curvature flow and surface diffusion (2025)
  (with Guangwei Gao, Buyang Li, Rong Tang)
  
   

• On a Cahn-Hilliard equation for the growth and division of chemically active droplets modeling protocells (2025)
  (with Kei Fong Lam, Robert Nürnberg, Andrea Signori)

   

• A convergent finite element method for two-phase Stokes flow driven by surface tension (2025)
  (with Genming Bai, Shravan Veerapaneni) 
   
• Error estimates for a surface finite element method for anisotropic mean curvature flow (2025)
  (with Klaus Deckelnick, Balázs Kovács)
  
   

in refereed journals:

• A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface (2026)
  Commun. Comput. Phys., Vol. 40, No. 4, pp. 992-1018
  (with Robert Nürnberg)
  PREPRINT

   

• Structure-preserving parametric finite element methods for two-phase Stokes flow based on Lagrange multiplier approaches
  Journal of Computational Physics. Volume 560 (2026), Article 114922
  (with Dennis Trautwein, Ganghui Zhang)
  PREPRINT
   
• Convergence analysis for the Barrett–Garcke–Nürnberg method of transport type for evolving curves
  (with Genming Bai, Shravan Veerapaneni)
  Numerische Mathematik (2026) 158:361–41
  PREPRINT
   

• An energy-stable parametric finite element method for Willmore flow with normal-tangential velocity splitting 
  SIAM Journal on Scientific Computing, Vol. 48, Iss. 3 (2026), 10.1137/25M1773878
  (with Robert Nürnberg, Quan Zhao)
  PREPRINT

   

• Stable fully practical finite element methods for axisymmetric Willmore flow
  Computers & Mathematics with Applications, Volume 212, 2026, 128-145
  (with Robert Nürnberg, Quan Zhao)
  doi.org/10.1016/j.camwa.2026.03.028
  PREPRINT

   

• Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness
  J. Evol. Equ. 26, 47 (2026)
  (with Helmut Abels, Andrea Poiatti)
  PREPRINT

   

• The anisotropic Cahn--Hilliard equation with degenerate mobility: Existence of weak solutions
  Analysis and Applications (2026), 1-16
  (with Patrik Knopf, Andrea Signori)
  doi.org/10.1142/S0219530526500144 PREPRINT

   

• An energy-stable minimal deformation rate scheme for mean curvature flow and surface diffusion
  SIAM Journal on Scientific Computing (2026), Vol. 49, 1, A103-A131
  (with Guangwei Gao, Buyang Li, Rong Tang)
  doi.org/10.1137/25M1753838
  PREPRINT

   

• Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions
  Journal of Mathematical Fluid Mechanics, Vol. 28, article no. 7 (2026)
  (with Helmut Abels, Julia Wittmann)
  PREPRINT

   

• Structure-preserving parametric finite element method for curve diffusion based on Lagrange multiplier approaches
  SIAM Journal on Science Computing, Vol. 47, Iss.3 (2025) 
  (with Wei Jiang, Chunmei Su, Ganghui Zhang)
  PREPRINT
   
• A finite element method for anisotropic crystal growth on surfaces
  Int. J. Numer. Anal. Model. 22 (2025), no. 5, 614–636.
  (with Robert Nürnberg)
  doi.org/10.4208/ijnam2025-1027
  PREPRINT

• Structure-preserving parametric finite element method for surface diffusion based on Lagrange multiplier approaches
  SIAM J. Sci. Comput. 47 (2025), no. 3, A1983–A2011
  (with Wei Jiang, Chumei Su, Ganghui Zhang)
  doi.org/10.1137/24M168754
  PREPRINT

   

• On a diffuse interface model for diblock copolymers interacting with an electric field
  Communications in Mathematical Sciences, Volume 24 (2026) Number 1, pp.43-105
  (with Helmut Abels, Andrea Di Primio)
  dx.doi.org/10.4310/CMS.260102230537
   

• A parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions
  Comput. Methods Appl. Math. (2026), 26(1), 43–67
  (with Tokuhiro Eto, Robert Nürnberg)
  doi.org/10.1515/cmam-2025-0080
  PREPRINT

   

• A variational front-tracking method for multiphase flow with triple junctions
  Mathematics of Computation (2025), 1-36>
  (with Robert Nürnberg, Quan Zhao)
  doi.org/10.1090/mcom/4078
  PREPRINT

   

• Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Global Well-Posedness
  Calculus of Variations ans Partial Differential Equations, Volume 64, article number 141 (2025)
  (with Helmut Abels, Andrea Poiatti)
  doi.org/10.1007/s00526-025-03001-w
  PREPRINT

   

• Parametric finite element approximation of two-phase Navier--Stokes flow with viscoelasticity
  IMA Journal of Numerical Analysis, 46, 149–204 (2026)
  (with Robert Nürnberg, Dennis Trautwein)
  doi.org/10.1093/imanum/drae103
  PREPRINT

   

• Isoparametric finite element methods for mean curvature flow and surface diffusion
  Journal of Computational Physics, Vol. 539, 114248 (2025)
  (with Robert Nürnberg, Simon Praetorius, Ganghui Zhang)
  doi.org/10.1016/j.jcp.2025.114248
  PREPRINT

   

• Corrigendum to: Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport
  Journal of Numerical Mathematics, vol. 32, no. 2, 2024, pp. 213-214
  (with Dennis Trautwein)
  doi.org/10.1515/jnma-2024-0035
  PREPRINT
   
• Existence of Weak Solutions to a Cahn-Hilliard-Biot System
  Nonlinear Analysis: Real World Applications, Vol. 81, February 2025, 104194
  (with Helmut Abels, Jonas Haselböck)
  doi.org/10.1016/j.nonrwa.2024.104194
  PREPRINT

• Stable fully discrete finite element methods with BGN tangential motion for Willmore flow of planar curves
  J. Sci. Comput. 105 (2025), no. 2, Paper No. 45, 23 pp.
  (with Robert Nürnberg, Quan Zhao)
  doi.org/10.1007/s10915-025-03068-9
  PREPRINT

   

• A structure-preserving finite element method for the multi-phase Mullins-Sekerka problem with triple junctions
  Numerische Mathematik (2024)
  (with Tokuhiro Eto, Robert Nürnberg)
  doi.org/10.1007/s00211-024-01414-x
  PREPRINT

   

• Complex pattern formation governed by a Cahn-Hilliard-Swift-Hohenberg system: Analysis and numerical simulations (2024)
  Mathematical Models & Methods in Applied Sciences
  doi.org/10.1142/S021820252450043X
  (with Kei Fong Lam, Robert Nürnberg, Andrea Signori)
  PREPRINT

   

• Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities (2024)
  Mathematische Annalen (2024) 389:1267–1321
  (with Helmut Abels, Andrea Giorgini)
  doi.org/10.1007/s00208-023-02670-2
  PREPRINT
   

• Mathematical Analysis of a Diffuse Interface Model for Multi-Phase Flows of Incompressible Viscous Fluids with Different Densities
  Math. Fluid Mech.26, no.2, Paper No. 29.(2024)
  doi.org/10.1007/s00021-024-00864-5
  (with Helmut Abels, Andrea Poiatti)
  PREPRINT

   

• Arbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flow
  Computers & Mathematics with Applications, Vol. 155, 209-223, (2024)
  doi.org/10.1016/j.camwa.2023.12.013
  (with Robert Nürnberg, Quan Zhao)
  PREPRINT

in refereed journals:

• A variational front-tracking method for multiphase flow with triple junctions
  Mathematics of Computation (2025), 1-36>
  (with Robert Nürnberg, Quan Zhao)
  doi.org/10.1090/mcom/4078
  PREPRINT
   
• Stable fully practical finite element methods for axisymmetric Willmore flow
  Computers & Mathematics with Applications, Volume 212, 2026, 128-145
  (with Robert Nürnberg, Quan Zhao)
  doi.org/10.1016/j.camwa.2026.03.028
  PREPRINT
   
• Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness
  J. Evol. Equ. 26, 47 (2026)
  (with Helmut Abels, Andrea Poiatti)
  PREPRINT
   
• The anisotropic Cahn--Hilliard equation with degenerate mobility: Existence of weak solutions
  Analysis and Applications (2026), 1-16
  (with Patrik Knopf, Andrea Signori)
  doi.org/10.1142/S0219530526500144 PREPRINT
   
• An energy-stable minimal deformation rate scheme for mean curvature flow and surface diffusion
  SIAM Journal on Scientific Computing (2026), Vol. 49, 1, A103-A131
  (with Guangwei Gao, Buyang Li, Rong Tang)
  doi.org/10.1137/25M1753838
  PREPRINT
   
• Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions
  Journal of Mathematical Fluid Mechanics, Vol. 28, article no. 7 (2026)
  (with Helmut Abels, Julia Wittmann)
  PREPRINT
   
• Structure-preserving parametric finite element method for curve diffusion based on Lagrange multiplier approaches
  SIAM Journal on Science Computing, Vol. 47, Iss.3 (2025) (with Wei Jiang, Chunmei Su, Ganghui Zhang)
  PREPRINT
   
• On a diffuse interface model for diblock copolymers interacting with an electric field
  Communications in Mathematical Sciences, Volume 24 (2026) Number 1, pp.43-105
  (with Helmut Abels, Andrea Di Primio)
  dx.doi.org/10.4310/CMS.260102230537
   
• A parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions
  Comput. Methods Appl. Math. (2026), 26(1), 43–67
  (with Tokuhiro Eto, Robert Nürnberg)
  doi.org/10.1515/cmam-2025-0080
  PREPRINT
   
• Isoparametric finite element methods for mean curvature flow and surface diffusion
  Journal of Computational Physics, Vol. 539, 114248 (2025)
  (with Robert Nürnberg, Simon Praetorius, Ganghui Zhang)
  doi.org/10.1016/j.jcp.2025.114248
  PREPRINT
   
• Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Global Well-Posedness
  Calculus of Variations ans Partial Differential Equations, Volume 64, article number 141 (2025)
  (with Helmut Abels, Andrea Poiatti)
  doi.org/10.1007/s00526-025-03001-w
  PREPRINT
   
• Parametric finite element approximation of two-phase Navier--Stokes flow with viscoelasticity
  IMA Journal of Numerical Analysis, 46, 149–204 (2026)
  (with Robert Nürnberg, Dennis Trautwein)
  doi.org/10.1093/imanum/drae103
  PREPRINT
   
• Existence of Weak Solutions to a Cahn-Hilliard-Biot System
  Nonlinear Analysis: Real World Applications, Vol. 81, February 2025, 104194
  (with Helmut Abels, Jonas Haselböck)
  doi.org/10.1016/j.nonrwa.2024.104194
  PREPRINT
   
• A structure-preserving finite element method for the multi-phase Mullins-Sekerka problem with triple junctions
  Numerische Mathematik (2024)
  (with Tokuhiro Eto, Robert Nürnberg)
  doi.org/10.1007/s00211-024-01414-x
  PREPRINT
   
• Complex pattern formation governed by a Cahn-Hilliard-Swift-Hohenberg system: Analysis and numerical simulations (2024)
  Mathematical Models & Methods in Applied Sciences
  doi.org/10.1142/S021820252450043X
  (with Kei Fong Lam, Robert Nürnberg, Andrea Signori)
  PREPRINT
   
• Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities (2024)
  Mathematische Annalen (2024) 389:1267–1321
  (with Helmut Abels, Andrea Giorgini)
  doi.org/10.1007/s00208-023-02670-2
  PREPRINT
   
• Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structuress
  Appl. Math. Optim. 89, no. 1, Paper No. 24, 58 pp., (2023)
  doi.org/10.1007/s00245-023-10093-3
  (with Paul Hüttl, Christian Kahle, Patrik Knopf)
  PREPRINT
   
• A Cahn-Hilliard phase field model coupled to an Allen-Cahn model of viscoelasticity at large strains
  Nonlinearity 36, no.12, 6589–6638.(2023)
  doi.org/10.48550/arXiv.2301.08341
  (with Abramo Agosti, Pierluigi Colli, Elisabetta Rocca)
  PREPRINT
   
• Mathematical Analysis of a Diffuse Interface Model for Multi-Phase Flows of Incompressible Viscous Fluids with Different Densities
  Math. Fluid Mech.26, no.2, Paper No. 29.(2024)
  doi.org/10.1007/s00021-024-00864-5
  (with Helmut Abels, Andrea Poiatti)
  PREPRINT
   
• A Cahn-Hilliard model coupled to viscoelasticity with large deformations
  Commun. Math. Sci. 21, no. 8, 2083–2130, (2023)
  doi.org/10.4310/CMS.2023.v21.n8.a2
  (with Abramo Agosti, Pierluigi Colli, Elisabetta Rocca)
  PREPRINT
   
• Arbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flow
  Computers & Mathematics with Applications, Vol. 155, 209-223, (2024)
  doi.org/10.1016/j.camwa.2023.12.013
  (with Robert Nürnberg, Quan Zhao)
  PREPRINT
   
• Approximation and existence of a viscoelastic phase-field model for tumour growth in two and three dimensions
  Discrete and Continuous Dynamical Systems - S. (2023),
  doi: 10.3934/dcdss.2023181
  (with Dennis Trautwein)
  PREPRINT
   
• The anisotropic Cahn-Hilliard equation: regularity theory and strict separation properties, Discrete and Continuous Dynamical Systems
  Series S (2023),
  doi:10.3934/dcdss.2023146
  (with Patrik Knopf, Julia Wittmann)
  PREPRINT
   
• Unfitted Finite Element Methods for Axisymmetric Two-Phase Flow
  J Sci Comput 97, 14 (2023),
  doi.org/10.1007/s10915-023-02325-z
  (with Robert Nürnberg, Quan Zhao)
  PREPRINT
   
• Sharp interface analysis of a diffuse interface model for cell blebbing with linker dynamics
  ZAMM Z. Angew. Math. Mech.103, no.12, Paper No. e202300101, 39 pp.(2023)
  doi.org/10.1002/zamm.202300101
  (with Philipp Nöldner, Martin Burger)
  PREPRINT
   
• Structure-preserving discretizations of two-phase Navier-Stokes flow using fitted and unfitted approaches
  Journal of Computational Physics 112276 (2023),
  doi.org/10.1016/j.jcp.2023.112276
  (with Robert Nürnberg, Quan Zhao)
  PREPRINT
   
• Phase field topology optimisation for 4D printing
  ESAIM Control Optim. Calc. Var. 29 (24) 46 pp. (2023),
  doi.org/10.1051/cocv/2023012
  (with Kei Fong Lam, Robert Nürnberg, Andrea Signori)
  PREPRINT
   
• Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies
  Applied Mathematics & Optimization 87:44, (2023),
  doi.org/10.1007/s00245-022-09939-z
  (with Kei Fong Lam, Robert Nürnberg, Andrea Signori)
  PREPRINT
   
• Phase-field methods for spectral shape and topology optimization
  ESAIM COCV 29 (10), 57 pp. (2023),
  doi.org/10.1051/cocv/2022090
  (with Paul Hüttl, Christian Kahle, Patrik Knopf, Tim Laux)
  PREPRINT
   
• A diffuse-interface approach for solid-state dewetting with anisotropic surface energies
  Journal of Nonlinear Science 33, 34 (2023),
  doi.org/10.1007/s00332-023-09889-y
  (with Patrik Knopf, Robert Nürnberg, Quan Zhao)
  PREPRINT
   
• Qualitative properties for a system coupling scaled mean curvature flow and diffusion
  Journal of Differential Equations 349 236-268 (2023),
  doi.org/10.1016/j.jde.2022.12.019
  (with Helmut Abels, Felicitas Bürger)
  PREPRINT
   
• Short time existence for coupling of scaled mean curvature flow and diffusion
  J. Evol. Equ. 23:14 (2023),
  doi.org/10.1007/s00028-022-00861-z
  (with Helmut Abels, Felicitas Bürger)
  PREPRINT
   
• A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters
  Numer. Methods Partial Differential Eq. 39 (1) 759-794 (2023),
  doi.org/10.1002/num.22921
  (with Weizhu Bao, Robert Nürnberg, Quan Zhao)
  PREPRINT
   
• A phase-field approach to shape and topology optimization of acoustic waves in dissipative media
  SIAM Journal on Control and Optimization 60 (4) (2022),
  doi.org/10.1137/21M1449294
  (with Sourav Mitra and Vanja Nikolić)
  PREPRINT
   
• Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces
  Numerische Mathematik 151, 873-925 (2022),
  doi.org/10.1007/s00211-022-01301-3
  (with Charles M. Elliott, Balázs Kovács)
  PREPRINT
   
• Viscoelastic Cahn-Hilliard models for tumour growth
  Mathematical Models and Methods in Applied Sciences 32 (13), 2673-2758 (2022),
  doi.org/10.1142/S0218202522500634
  (with Balázs Kovács, Dennis Trautwein)
  PREPRINT
   
• Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport
  Journal of Numerical Mathematics, vol. 30, no. 4, pp. 295-324 (2022),
  doi.org/10.1515/jnma-2021-0094
  (with Dennis Trautwein)
  PREPRINT
   
• A diffuse interface model for cell blebbing including membrane-cortex coupling with linker dynamics
  SIAM J. Appl. Math. 82 (3), 1091-1112 (2022),
  doi:10.1137/21M1433642
  (with Philipp Werner, Martin Burger and Florian Frank)
  PREPRINT
   
• Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations
  J. Comput. Phys. 460 (111180), 23 pp. (2022),
  doi.org/10.1016/j.jcp.2022.111180
  (with Weizhu Bao, Robert Nürnberg, Quan Zhao)
  PREPRINT
   
• Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids
  Calc. Var. 61:179 (2022),
  doi.org/10.1007/s00526-022-02271-y
  (with Patrik Knopf, Sourav Mitra and Anja Schlömerkemper)
  PREPRINT
   
• Stability analysis for stationary solutions of the Mullins-Sekerka flow with boundary contact
  Mathematische Nachrichten, 295: 683-705 (2022),
  doi.org/10.1002/mana.201900303
  (with Maximilian Rauchecker)
  PREPRINT
   
• Long-time dynamics of the Cahn--Hilliard equation with kinetic rate dependent dynamic boundary conditions
  Nonlinear Analysis 215, 112619 (2022),
  doi.org/10.1016/j.na.2021.112619
  (with Patrik Knopf and Sema Yayla)
  PREPRINT
   
• Standard planar double bubbles are stable under surface diffusion flow
  Communications in Analysis and Geometry 29 (5), 1007-1060 (2021),
  dx.doi.org/10.4310/CAG.2021.v29.n5.a1
  (with Helmut Abels and Nasrin Arab)
  PREPRINT
   
• Non-linear stability of double bubbles under surface diffusion
  Journal of Differential Equations 302, 617-661 (2021),
  doi.org/10.1016/j.jde.2021.08.033
  (with Michael Gößwein)
  PREPRINT
   
• Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds
  Numer. Math. 149, 375-415 (2021),
  375 doi.org/10.1007/s00211-021-01231-6
  (with Robert Nürnberg)
  PREPRINT
   
• Sparse optimal control of a phase field tumour model with mechanical effects
  SIAM J. Control. Optim. 59 (2), 1555-1580 (2021),
  doi.org/10.1137/20M1372093
  (with Kei Fong Lam and Andrea Signori)
  PREPRINT
   
• Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
  Advances in Nonlinear Analysis, vol. 11, no. 1, pp. 159-197 (2022),
  doi.org/10.1515/anona-2020-0183
  (with Paul Hüttl and Patrik Knopf)
  PREPRINT
   
• Stable approximations for axisymmetric Willmore flow for closed and open surfaces
  ESAIM: M2AN55, 833-885 (2021),
  doi.org/10.1051/m2an/2021014
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Cahn-Hilliard-Brinkman systems for tumour growth
  Discrete & Continuous Dynamical Systems Series S 14 (11), 3989-4033 (2021),
  doi: 10.3934/dcdss.2021034
  (with Matthias Ebenbeck and Robert Nürnberg)
  PREPRINT
   
• On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects
  Nonlinear Analysis: Real World Application 57 1031922019 (2020),
  doi.org/10.1016/j.nonrwa.2020.103192
  (with Kei Fong Lam and Andrea Signori)
  PREPRINT
   
• Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes
  IMA Journal of Numerical Analysis 00, 1-42 (2020),
  doi.org/10.1093/imanum/draa027
  (with Robert Nürnberg)
  PREPRINT
   
• Long-time dynamics for a Cahn-Hilliard tumor growth model with chemotaxis
  Z. Angew. Math. Phys. 71, 123 (2020),
  doi.org/10.1007/s00033-020-01351-3
  (with Sema Yayla)
  PREPRINT
   
• Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data
  Math. Meth. Appl. Sci. 43 (15), 8945-8979 (2020),
  DOI: 10.1002/mma.6588
  (with Abramo Agosti, Pasquale Ciarletta and Michael Hinze)
  PREPRINT
   
• Long time existence of solutions to an elastic flow of networks
  Communications in Partial Differential Equations 45 (10), 1253-1305 (2020),
  DOI: 10.1080/03605302.2020.1771364
  (with Julia Menzel and Alessandra Pluda)
  PREPRINT
   
• On the surface diffusion flow with triple junctions in higher space dimensions
  Geometric Flows 5 (1), 1-39 (2020),
  DOI: 10.1515/geofl-2020-0001
  (with Michael Gößwein)
  PREPRINT
   
• On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces
  J. Evol. Equ. 21, 201-224 (2021),
  doi.org/10.1007/s00028-020-00575-0
  (with Bogdan-Vasile Matioc)
  PREPRINT
   
• Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: A gradient flow approach
  SIAM J. Math. Anal. 52 (1), 340-369 (2020),
  doi.org/10.1137/19M1258840
  (with Patrik Knopf)
  PREPRINT
   
• Parametric finite element approximations of curvature-driven interface evolutions
  Handbook of Numerical Analysis 21, 275-423 (2020),
  doi.org/10.1016/bs.hna.2019.05.002
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Analysis of Cahn-Hilliard-Brinkman models for tumour growth
  PAMM • Proc. Appl. Math. Mech. 19:e201900021, (2019),
  DOI: 10.1002/pamm.201900021
  (with Matthias Ebenbeck)
  PREPRINT
   
• Numerical approximation of curve evolutions in Riemannian manifolds
  IMA Journal of Numerical Analysis 40 (3), 1601-1651, drz012 (2019),
  doi.org/10.1093/imanum/drz012
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Stable discretizations of elastic flow in Riemannian manifolds
  SIAM Journal on Numerical Analysis 2019 57:4, 1987-2018,
  doi.org/10.1137/18M1227111
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• On a Cahn-Hilliard-Brinkman model for tumour growth and its singular limits
  SIAM J. Math. Anal. 51 (3), 1868-1912 (2019),
  doi.org/10.1137/18M1228104
  (with Matthias Ebenbeck)
  PREPRINT
   
• Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants
  Comm. Pure Appl. Anal. 18 (1), 195-225 (2019),
  Doi: 10.3934/cpaa.2019011
  (with Helmut Abels and Josef Weber)
  PREPRINT
   
• Optimal control of time-discrete two-phase flow driven by a diffuse-interface model
  ESAIM: COCV 25 (13) (2019),
  DOI: 10.1051/cocv/2018006
  (with Michael Hinze and Christian Kahle)
  PREPRINT
   
• Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis
  Journal Differential Equations 266 (9), 5998-6036 (2019),
  doi.org/10.1016/j.jde.2018.10.045
  (with Matthias Ebenbeck)
  PREPRINT
   
• Variational discretization of axisymmetric curvature flows
  Numerische Mathematik 141 (3), 791-837 (2019),
  doi.org/10.1007/s00211-018-1013-z
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Finite element methods for fourth order axisymmetric geometric evolution equations
  Journal of Computational Physics 376, 733--766 (2019),
  doi.org/10.1016/j.jcp.2018.10.006
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Willmore flow of planar networks
  Journal of Differential Equations 266 (4), 2019-2051 (2019),
  doi.org/10.1016/j.jde.2018.08.019
  (with Julia Menzel and Alessandra Pluda)
  PREPRINT
   
• Cahn--Hilliard inpainting with the double obstacle potential
  SIAM J. Imaging Sciences 11 (3), 2064--2089 (2018),
  doi.org/10.1137/18M1165633
  (Kei Fong Lam and Vanessa Styles)
  PREPRINT
   
• Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation
  SMAI J. Comput. Math. 4, 151-195 (2018),
  doi: 10.5802/smai-jcm.32
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• A phase field approach to shape optimization in Navier-Stokes flow with integral state constraint
  Adv. Comput. Math. 44 (5), 1345-1383 (2018),
  doi.org/10.1007/s10444-018-9586-8
  (with Michael Hinze and Christian Kahle and Kei Fong Lam)
  PREPRINT
   
• A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis
  Mathematical Models and Methods in Applied Sciences 28 (3), 525-577 (2018),
  DOI: 10.1142/S0218202518500148
  (with Kei Fong Lam, Robert Nürnberg and Emanuel Sitka)
  PREPRINT
   
• Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature
  IMA J. numer. Anal. 37 (4), 1657-1709 (2017),
  doi.org/10.1093/imanum/drx006
  (with John W. Barrett and Robert Nürnberg)
   
• Analysis of a Cahn-Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis
  Discrete Contin. Dyn. Syst. 37 (8), 4277-4308 (2017),
  10.3934/dcds.2017183
  (with Kei Fong Lam)
  PREPRINT
   
• Finite element approximation for the dynamics of fluidic two-phase biomembranes
  ESAIM: M2AN 51 (6), 2319-2366 (2017),
  doi.org/10.1051/m2an/2017037
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Segmentation of three-dimensional images with parametric active surfaces and topology changes
  J. Sci. Comput. 72, 1333-1367 (2017),
  doi.org/10.1007/s10915-017-0401-3
  (with Heike Benninghoff)
  PREPRINT
   
• Optimal control of treatment time in a diffuse interface model of tumor growth
  Appl. Math. Optim. 78 (3), 495-544 (2018),
  DOI 10.1007/s00245-017-9414-4
  (with Kei Fong Lam and Elisabetta Rocca)
  PREPRINT
   
• A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities
  J. Math. Fluid Mech. 20 (2), 531-567 (2018),
  DOI:10.1007/s00021-017-0334-5
  (with Luca Dedè and Kei Fong Lam)
  PREPRINT
   
• A volume-of-fluid method for three-dimensional hexagonal solidification processes
  Journal of Comp. Physics 339, 356-369 (2017),
  doi.org/10.1016/j.jcp.2017.03.001
  (with M. Reitzle, C. Kiefer-Roth and B. Weigand)
   
• Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth
  AIMS Mathematics 1 (3), 318-360 (2016),
  doi: 10.3934/Math.2016.3.318
  (with Kei Fong Lam)
  PREPRINT
   
• Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport
  European Journal of Applied Mathematics 28 (2), 284-316 (2017),
  doi.org/10.1017/S0956792516000292
  (with Kei Fong Lam)
  PREPRINT
   
• Image segmentation and restoration using parametric contours with free endpoints
  IEEE Trans. Image Process 25 (4), 1639-1648 (2016),
  doi: 10.1109/TIP.2016.2529180
  (with Heike Benninghoff)
  PREPRINT
   
• Finite element approximation for the dynamics of asymmetric fluidic biomembranes
  Math. Comp. 86, 1037-1069 (2017),
  dx.doi.org/10.1090/mcom/3162
  (with John W. Barrett and Robert Nürnberg)
   
• Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects
  SIAM J. Numer. Anal. 54 (3), 1732-1761 (2016),
  doi.org/10.1137/16M1065379
  (with John W. Barrett and Robert Nürnberg)
   
• Numerical computations of the dynamics of fluidic membranes and vesicles
  Phys. Rev. E 92, 052704 (2015),
  doi.org/10.1103/PhysRevE.92.052704
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Sharp interface limit for a phase field model in structural optimization
  SIAM J. Control Optim. 54 (3), 1558-1548 (2016),
  doi.org/10.1137/140989066
  (with Luise Blank, Claudia Hecht and Christoph Rupprecht)
  PREPRINT
   
• Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach
  Interfaces and Free Boundaries 18(2), 219-261 (2016),
  DOI 10.4171/IFB/363
  (with Claudia Hecht, Michael Hinze, Christian Kahle and Kei Fong Lam)
  PREPRINT
   
• A coupled surface-Cahn-Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes
  Math. Models Methods Appl. Sci. 26 (6), 1149-1189 (2016),
  doi.org/10.1142/S0218202516500275
  (with Johannes Kampmann, Andreas Rätz and Matthias Röger)
  PREPRINT
   
• A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport
  Math. Models Methods Appl. Sci. 26 (6), 1095-1148 (2016),
  doi.org/10.1142/S0218202516500263
  (with Kei Fong Lam, Emanuel Sitka and Vanessa Styles)
  PREPRINT
   
• A stable numerical method for the dynamics of fluidic membranes
  Numerische Mathematik 134 (4), 783-822 (2016),
  DOI 10.1007/s00211-015-0787-5
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension
  Math. Nachr. 289 (2-3), 136-174 (2016),
  DOI 10.1002/mana.201400102
  (with Helmut Abels and Lars Müller)
  PREPRINT
   
• Shape and topology optimization in Stokes flow with a phase field approach
  Applied Mathematics & Optimization 73 (1), 23-70 (2016),
  DOI 10.1007/s00245-015-9291-7
  (with Claudia Hecht)
  PREPRINT
   
• Segmentation and restoration of images on surfaces by parametric active contours with topology changes
  Journal of Mathematical Imaging and Vision 55 (1), 105-124 (2016),
  doi: 10.1007/s10851-015-0616-6
  (with Heike Benninghoff)
  PREPRINT
   
• A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow
  Applied Numerical Mathematics 99, 151-171 (2016),
  doi:10.1016/j.apnum.2015.09.002
  (with Michael Hinze and Christian Kahle)
  PREPRINT
   
• Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow
  ESAIM: Control, Optimisation and Calculus of Variations, 309-337, Vol. 22, (2) (2016),
  doi.org/10.1051/cocv/2015006
  (with Claudia Hecht)
  PREPRINT
• Stable numerical approximation of two-phase flow with a Boussinesq-scriven surface fluid
  Commun. Math. Sci. 13 (7), 1829-1874 (2014),
  doi.org/10.4310/CMS.2015.v13.n7.a9
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Numerical approximation of phase field based shape and topology optimization for fluids
  SIAM J. SCI. COMPUT. 37 (4), A1846-A1871 (2015),
  DOI 10.1137/140969269
  (with Claudia Hecht, Michael Hinze and Christian Kahle)
  PREPRINT
   
• On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions
  J. Evol. Equ. 15, 913-959 (2015),
  DOI 10.1007/s00028-015-0287-1
  (with Helmut Abels and Nasrin Arab)
  PREPRINT
   
• Stable finite element approximations of two-phase flow with soluble surfactant
  Journal of Computational Physics 297, 530-564 (2015),
  doi.org/10.1016/j.jcp.2015.05.029
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• On the stable numerical approximation of two-phase flow with insoluble surfactant
  ESAIM: M2AN 49, 421-458 (2015),
  doi.org/10.1051/m2an/2014039
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Stability of spherical caps under the volume-preserving mean curvature flow with line tension
  Nonlinear Anal: Theory, Methods & Applications, Vol. 117, 8-37 (2015),
  doi.org/10.1016/j.na.2014.11.020
  (with Helmut Abels and Lars Müller)
  PREPRINT
   
• A phase-field approach for wetting phenomena of multiphase droplets on solid surfaces
  Langmuir 30 (14), 4033-4039 (2014),
  doi.org/10.1021/la500312q
  (with Marouen Ben Said, Michael Selzer, Britta Nestler, Daniel Braun, Christian Greiner)
  copies are available by email request
   
• A stable parametric finite element discretization of two-phase Navier-Stokes flow
  J. Sci. Comput. 63 (1), 78-117 (2014),
  doi.org/10.1007/s10915-014-9885-2
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Efficient image segmentation and restoration using parametric curve evolution with junctions and topology changes
  SIAM J. IMAGING SCIENCES 7 (3), 1451-1483 (2014),
  doi.org/10.1137/130932430
  (with H. Benninghoff)
  PREPRINT
   
• Relating phase field and sharp interface approaches to structural topology optimization
  ESAIM: Control, Optimisation and Calculus of Variations 20(4), 1025-1058 (2014),
  doi.org/10.1051/cocv/2014006
  (with Luise Blank, M. Hassan Farshbaf-Shaker and Vanessa Styles)
  PREPRINT
   
• Stable phase field approximations of anisotropic solidification
  IMA J. Numer. Anal. 34 (4) 1289-1327 (2014),
  doi.org/10.1093/imanum/drt044
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Diffuse interface modelling of soluble surfactants in two-phase flow
  Comm. Math. Sci. 12 (8) 1475-1522 (2014),
  (with Kei Fong Lam and Björn Stinner)
  PREPRINT
   
• Mean curvature flow with triple junctions in higher space dimensions
  Archive for Rational Mechanics and Analysis 211, Issue 1 301-334 (2014),
  doi.org/10.1007/s00205-013-0668-y
  (with Daniel Depner and Yoshihito Kohsaka)
  PREPRINT
   
• Phase field models versus parametric front tracking methods: Are they accurate and computationally efficient?
  Published online by Cambridge University Press: 03 June 2015, Research Article, Communications in Computational Physics , Volume 15 , Issue 2, pp. 506 - 555, February (2014),
  doi:10.4208/cicp.190313.010813a
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow
  Comput. Methods Appl. Mech. Engrg. 267 511-530(2013),
  doi.org/10.1016/j.cma.2013.09.023
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Primal-dual active set methods for Allen-Cahn variational inequalities with non-local constraints
  Numer. Meth. PDEs 29 (3) 999-1030 (2013),
  doi.org/10.1002/num.21742
  (with Luise Blank, Lavinia Sarbu and Vanessa Styles)
  PREPRINT
   
• Curvature Driven Interface Evolution
  Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 115, Issue 2, 63-100. September (2013),
  DOI 10.1365/s13291-013-0066-2
  PREPRINT
   
• Finite element approximation of one-sided Stefan problems with anisotropic, approximately crystalline, Gibbs-Thomson law
  Adv. Differential Equations 18 383-432 (2013),
  DOI: 10.57262/ade/1360073021
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• On the stable discretization of strongly anisotropic phase field models with applications to crystal growth
  ZAMM Z. Angew. Math. Mech. 93 (10-11) 719-732 (2013),
  doi.org/10.1002/zamm.201200147
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility
  Ann. Inst. H. Poincaré Anal. Non Linéaire 30 1175-1190 (2013),
  doi.org/10.1016/j.anihpc.2013.01.002
  (with Helmut Abels and Daniel Depner)
  PREPRINT
   
• Linearized stability analysis of surface diffusion for hypersurfaces with triple lines
  Hokkaido Math. J. 42, no. 1 11-52 (2013),
  DOI: 10.14492/hokmj/1362406637
  (with Daniel Depner)
  PREPRINT
   
• Non-local Allen-Cahn systems: Analysis and a primal dual active set method
  IMA J. Numer. Anal. 33 (4) 1126-1155, (2013),
  DOI: 10.1093/imanum/drs039
  (with Luise Blank, Lavinia Sarbu, Vanessa Styles)
  PREPRINT
   
• Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities
  J. Math. Fluid Mech. 15 453-480 (2013),
  doi.10.1007/s00021-012-0118-x
  (with Helmut Abels and Daniel Depner)
  PREPRINT
   
• Elastic flow with junctions: Variational approximation and applications to nonlinear splines
  Math. Models Methods Appl. Sci. 22, 1250037 (2012),
  doi.org/10.1142/S0218202512500376
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Numerical computations of facetted pattern formation in snow crystal growth
  Physical Review E 86 (1) (2012),
  DOI: 10.1103/PhysRevE.86.011604
  (with John W. Barrett)
  PREPRINT
   
• Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities
  Mathematical Models and Methods in Applied Sciences (M3AS) 22, Issue: 3 (2012),
  DOI: 10.1142/S0218202511500138
  (with Helmut Abels and Günther Grün)y
  PREPRINT
   
• Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves
  Numer. Math. 120 489-542 (2012),
  doi.org/10.1007/s00211-011-0416-x
  (with J. W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law
  Adv. Math. Sci. Appl. 21 255-283 (2011)
  (with Stefan Schaubeck)
  PREPRINT
   
• Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biological membranes
  Discrete Contin. Dyn. Syst. Ser. S4 no. 2, 371-389 (2011)
  doi: 10.3934/dcdss.2011.4.371
  (with M. Hassan Farshbaf-Shaker)
  PREPRINT
   
• The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute
  Numer. Methods Partial Differential Equations 27 no. 1, 1-30 (2011),
  doi.org/10.1002/num.20637
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• An inhomogeneous, anisotropic, elastically modified Gibbs-Thomson law as singular limit of a diffuse interface model
  Proc. Appl. Math. Mech., 10: 519-520, (2010),
  doi.org/10.1002/pamm.201010252
  (with Christiane Kraus)
  PREPRINT
   
• Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation
  Proc. Roy. Soc. Edinburgh Sect. A 140 no. 4, 673-706 (2010),
  doi:10.1017/S0308210508000541
  (with Matthieu Alfaro, Danielle Hilhorst, Hiroshi Matano and Reiner Schätzle)
  PREPRINT
   
• On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth
  J. Comput. Phys. 229 Issue 18, 6270-6299 (2010),
  doi.org/10.1016/j.jcp.2010.04.039
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Finite element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering
  Euro. Jnl of Applied Mathematics 21 519-556 (2010),
  doi:10.1017/S0956792510000203
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
• Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies
  Interfaces and Free Boundaries 12 (2) 187-234 (2010),
  DOI 10.4171/IFB/232
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton methoda
  EASIM: Control, Optimisation and Calculus of Variations 17 (4)/ 941-954 (2011),
  DOI: 10.1051/cocv/2010032
  (with Luise Blank and Martin Butz)
  PREPRINT
   
• Surface diffusion with triple junctions: A stability criterion for stationary solutions
  Advances in Differential Equations 15 (5-6) 437-472 (2010),
  DOI: 10.57262/ade/1355854677
  (with Kazuo Ito and Yoshihito Kohsaka)
  PREPRINT
   
• Numerical approximation of gradient flows for closed curves in ℝ^d
  IMA J. Numer. Anal. 30 4-60, (2010),
  doi:10.1093/imanum/drp005
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Nonlinear stability of stationary solutions for curvature flow with triple junction   Correction
  Calculus of Variations and Partial Differential Equations, Hokkaido Mathematical Journal 38 731-769, (2009), EPrint Servers # 900(2008),
  DOI: 10.14492/hokmj/1258554242
  (with Yoshihito Kohsaka and Daniel Sevcovic)
  PREPRINT
   
• Stability analysis of phase boundary motion by surface diffusion with triple junction
  Banach Center Publications 86 83-101 (2009),
  (with Kazuo Ito and Yoshihito Kohsaka)
  PREPRINT
   
• Parametric approximation of Willmore flow and related geometric evolution equations
  SIAM J. Sci. Comp. 31, no. 1 225-253 (2008),
  doi.org/10.1137/070700231
  (with John W. Barrett and Robert Nürnberg )
   
• Phase-field model for multiphase systems with preserved volume fractions
  Phys. Rev. E 78, 011604 (2008),
  DOI: 10.1103/PhysRevE.78.011604
  (with Britta Nestler, Michael Selzer and Björn Stinner and Frank Wendler)
  PREPRINT
   
• Allen-Cahn systems with volume constraints
  Mathematical Models and Methods in Applied Sciences (M3AS), 18, Issue: 8 1347-1381, (2008),
  DOI: 10.1142/S0218202508003066
  (with Britta Nestler, Björn Stinner and Frank Wendler)
  PREPRINT
   
• Nonlinear stability of stationary solutions for surface diffusion with boundary conditions
  SIAM J. Math. Anal. 40, no.2 491-515 (2008),
  doi.org/10.1137/07069475
  (with Kazuo Ito and Yoshihito Kohsaka)
  PREPRINT
   
• The Γ-limit of the Ginzburg-Landau energy in an elastic medium
  AMSA 18 345-379 (2008),
  PREPRINT
   
• On the parametric finite element approximation of evolving hypersurfaces in R³
  J. Comput. Phys. 227 4281-4307 (2008),
  (with John W. Barrett and Robert Nürnberg)
  doi.org/10.1016/j.jcp.2007.11.023
  PREPRINT
   
• A variational formulation of anisotropic geometric evolution equations in higher dimensions
  Springer Link, Numerische Mathematik 109 1-44 (2008),
  doi.org/10.1007/s00211-007-0135-5
  (with John W. Barrett and Robert Nürnberg)
   
• On sharp interface limits of Allen-Cahn/Cahn-Hilliard variational inequalities
  Discrete and Continuous Dynamical Systems Series S 1 (1) 1-14 (2008),
  DOI: 10.3934/dcdss.2008.1.1
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Numerical approximation of anisotropic geometric evolution equations in the plane
  IMA Journal of Numerical Analysis 28 (2) 292-330 (2008),
  doi.org/10.1093/imanum/drm013
  (with John W. Barrett and Robert Nürnberg)
   
• Stress and diffusion induced interface motion: Modelling and numerical simulations
  European Journal of Applied Math. 18 631-657 (2007),
  doi:10.1017/S095679250700719X
  (with Robert Nürnberg and Vanessa Styles)
   
• On the variational approximation of combined second and fourth order geometric evolution equations
  SIAM J. Scientific Comput. 29, Issue 3 1006-1041 (2007),
  doi.org/10.1137/060653974
  (with John W. Barrett and Robert Nürnberg)
   
• A phase field model for the electromigration of intergranular voids
  Interfaces and Free Boundaries 9 171-210 (2007),
  DOI 10.4171/IFB/161
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• A parametric finite element method for fourth order geometric evolution equations
  Journal of Computational Physics 222, Issue 1 441-467 (2007),
  doi.org/10.1016/j.jcp.2006.07.026
  (with John W. Barrett and Robert Nürnberg)
  PREPRINT
   
• Second order phase field asymptotics for multi-component systems
  Interfaces and Free Boundaries 8 131-157 (2006),
  DOI: 10.4171/IFB/138
  (with Björn Stinner)
  PREPRINT
   
• Surfactant spreading on thin viscous films: Nonnegative solutions of a coupled degenerate system
  SIAM J. Math. Analysis 37 (6) 2025-2048(2006),
  doi.org/10.1137/040617017
  (with Sandra Wieland)
  PREPRINT
   
• Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid
  Math. Comp. 75 7-41 (2006),
  (with John W. Barrett and R. Nürnberg)
  PREPRINT
   
• Mechanical effects in the Cahn-Hilliard model: A review on mathematical results
  in ``Mathematical Methods and Models in phase transitions'', ed.: Alain Miranville, Nova Science Publ. 43-77 (2005),
  PREPRINT
   
• Numerical approximation of the Cahn-Larché equation
  Numer. Math. 100, Number 4, 639 - 662 (2005),
  doi.org/10.1007/s00211-004-0578-x
  (with U. Weikard)
  PREPRINT
   
• Multicomponent alloy solidification: Phase-field modelling and simulations
  Phys. Reviews E, Vol. 71, No. 4 041609-1-6, (2005),
  doi.org/10.1103/PhysRevE.71.041609
  (with Britta Nestler and Björn Stinner)
  PREPRINT
   
• Linearized stability analysis of stationary solutions for surface diffusion with boundary conditions
  SIAM J. Math. Anal. 36, No. 4, 1031-1056 (2005),
  doi.org/10.1137/S0036141003437939
  (with K. Ito and Y. Kohsaka)
  PREPRINT
   
• On a Cahn-Hilliard model for phase separation with elastic misfit
  Ann. de l'IHP - Analyse non linéaire 22 (2) 165-185 (2005),
  doi.org/10.1016/j.anihpc.2004.07.001
  PREPRINT
   
• Bi-directional diffusion induced grain boundary motion with triple junctions
  Interfaces and Free Boundaries 6, (3), 271-294 (2004),
  DOI 10.4171/IFB/100
  (with Vanessa Styles)
   
• A diffuse interface model for alloys with multiple components and phases
  SIAM J. Appl. Math. 64 (3) 775-799 (2004),
  doi.org/10.1137/S0036139902413143
  (with B. Nestler and B. Stinner)
   
• Finite element approximation of surfactant spreading on a thin film
  SIAM J. Num. Anal. 41 1427-1464 (2003),
  doi.org/10.1137/S003614290139799X
  (with J. Barrett and R. Nürnberg)
   
• Exponential stability for a mirror-symmetric three phase boundary motion by surface diffusion
  Mathematische Nachrichten 257 3-15 (2003),
  doi.org/10.1002/mana.200310074
  (with J. Escher and K. Ito).
   
• Transient coarsening behaviour in the Cahn-Hilliard model
  Acta Mat. 51, 2823-2830, (2003),
  doi.org/10.1016/S1359-6454(03)00087-9
  (with B. Niethammer, M. Rumpf, U. Weikard)
   
• Modelling of microstructure formation and interface dynamics
  Comp. Mater. Sci 26, 111-119, (2003),
  doi.org/10.1016/S0927-0256(02)00407-X
  (with B. Nestler, Adam A. Wheeler)
   
• A Phase-field model for the solidification process in multicomponent alloys
  In: Emmerich, H., Nestler, B., Schreckenberg, M. (eds) Interface and Transport Dynamics.
  Lecture Notes in Computational Science and Engineering, vol 32. pp 142-149 Springer (2003)
  doi.org/10.1007/978-3-662-07969-0_12
  (with B. Nestler, B. Stinner)
   
• On Cahn-Hilliard systems with elasticity
  Proc. Roy. Soc. Edinburgh , 133 A, 307-331, (2003),
  doi:10.1017/S0308210500002419
   
• On fully practical finite element approximations of degenerate Cahn-Hilliard systems
  Math. Model. Num. Anal. (M2AN), Vol. 35 No. 4, 713-748, (2001),
  doi.org/10.1051/m2an:2001133
  (with J.W. Barrett and J.F. Blowey).
   
• A Phase field model for continuous clustering on vector fields
  IEEE Transactions on Visualization and Computer Graphics (TVCG), 7, 230-241, (2001),
  doi: 10.1109/2945.942691
  (with T. Preußer, M. Rumpf, A. Telea, U. Weikard and J. van Wijk).
   
• The Cahn-Hilliard equation with elasticity: Finite element approximation and qualitative studies
  Interfaces and Free Boundaries, 3, 101-118, (2001),
  DOI: 10.4171/IFB/34
  (with M. Rumpf and U.Weikard).
   
• A mathematical model for grain growth in thin metallic films
  Math. Models and Methods in Applied Sciences, Vol. 10, No. 6, 895-921, (2000),
  doi.org/10.1142/S021820250000046X
  (with B. Nestler)
   
• A singular limit for a system of degenerate Cahn-Hilliard equations
  Adv. in Diff. Equations, 5, No. 4-6, 401-434, (2000),
  doi.org/10.57262/ade/1356651336
  (with A. Novick-Cohen)
   
• A multi phase field concept: numerical simulations of moving phase boundaries and multiple junctions
  SIAM J. Appl. Math., Vol. 60, No.1, 295-315, (1999),
  doi.org/10.1137/S0036139998334895
  (with B. Nestler and B. Stoth)
   
• Finite element approximation of the Cahn-Hilliard equation with degenerate mobility
  SIAM J. Num. Anal., Vol 37, No.1, 286-318, (1999),
  doi.org/10.1137/S0036142997331669
  (with J.W. Barrett and J.F. Blowey).
   
• Anisotropy in multiphase sytems:a phase-field approach
  Interfaces and Free Boundaries, Vol. 1, No. 2, 175-198 (1999),
  DOI 10.4171/IFB/8
  (with B. Nestler and B. Stoth)
   
• Solutions of a fourth order degenerate parabolic equation with weak initial trace
  Ann. Scuola Normale Superiore Pisa Cl. (4), Vol. 28, No. 1, 153-181 (1999),
  (with R. Dal Passo)
   
• Finite element approximation of a fourth order nonlinear degenerate parabolic equation
  Numer. Math., Vol. 80, No. 4, 525-556, (1998),
  doi.org/10.1007/s002110050377
  (with J.W. Barrett and J.F. Blowey)
   
• On anisotropic order parameter models for multi-phasesystems and their sharp interface limits
  Physica D, Vol. 115, 87-108, (1998),
  doi.org/10.1016/S0167-2789(97)00227-3
  (with B. Nestler and B. Stoth)
   
• The degenerate multiphase Stefan problem with Gibbs-Thomson law
  Adv. Math. Sci. Appl. 8, No. 2, 929-941, (1998),
  (with T. Sturzenhecker)
   
• The thin viscous flow equation in higher space dimensions
  Adv. in Diff. Equations Vol. 3, No. 3, 417-440, (1998),
  DOI: 10.57262/ade/1366399848
  (with M. Bertsch, R. Dal Passo and G. Grün)
  PDF
   
• A multi-phase Mullins-Sekerka system: matched asymptotic expansions and an implicit time discretization for the geometric evolution problem
  Proc. Roy. Soc. Edinburgh 128 A, 481-506, (1998),
  (with L. Bronsard and B. Stoth)
   
• On a fourth order degenerate parabolic equation: global entropyestimates and qualitative behaviour of solutions
  SIAM J. Math. Anal. 29 (2), 321-342, (1998),
  doi.org/10.1137/S0036141096306170
  (with R. Dal Passo and G. Grün)
   
• Diffusional phase transitions in multicomponentsystems with a concentration dependent mobility matrix
  Physica D, Vol. 109, 242 - 256, (1997),
  doi.org/10.1016/S0167-2789(97)00066-3
  (with C.M. Elliott)
   
• Existence results for diffusive surface motion laws
  Adv. Math. Sci. Appl 7, No.1, 465-488, (1997),
  (with C.M. Elliott)
  PREPRINT
   
• On the Cahn-Hilliard equation with degenerate mobility
  SIAM J. Math. Anal. 27, 404-423, (1996),
  doi.org/10.1137/S0036141094267662
  (with C.M. Elliott)
   
• Travelling wave solutions as dynamic phase transitions in shape memory alloys
  J. Differential Equations, Vol. 121, No. 1, 203-231 (1995),
  doi.org/10.1006/jdeq.1995.1127

refereed book contributions:

• Diffuse interface approaches in atmosphere and ocean - modeling and numerical implementation
  Eden, Carsten, Iske, Armin (Eds.): Mathematics of Planet Earth 1, Energy Transfers in Atmosphere and Ocean, Springer Nature Switzerland 287-307 (2019),
  doi.org/10.1007/978-3-030-05704-6_9
  (with Michael Hinze and Christian Kahle)
  PREPRINT
   
• On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms
  Rocca, Elisabetta, Stefanelli, Ulisse, Truskinovsky, Lev, Visintin, Augusto (Eds.): Trends in applications of mathematics to mechanics 243-264,
  Springer INdAM Ser. 27, Springer Cham (2018),
  doi.org/10.1007/978-3-319-75940-1_12
  (with Kei Fong Lam)
  PREPRINT
   
• Diffuse interface models for incompressible two-phase flows with different densities
  Bothe, Dieter, Reusken, Arnold (Eds.): Transport Processes at Fluidic Interfaces, 203-229 (2017), Adv. Math. Fluid Mech., Springer / Birkhäuser, Cham
  doi.org/10.1007/978-3-319-56602-3_8
  (with Helmut Abels, Günther Grün and Stefan Metzger)
  PREPRINT
   
• Two-phase flow with surfactants: Diffuse interface models and their analysis
  Bothe, Dieter, Reusken, Arnold (Eds.): Transport Processes at Fluidic Interfaces, 255-270 (2017), Springer
  doi.org/10.1007/978-3-319-56602-3_10
  (with Helmut Abels, Kei Fong Lam and Josef Weber)
  PREPRINT
   
• Weak solutions and diffuse interface models for incompressible two-phase flows
  appeared in Y. Giga, A. Novotny (eds.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018),
  doi.org/10.1007/978-3-319-13344-7_29
  (with Helmut Abels)
  PREPRINT
   
• A phase field approach for shape and topology optimization in Stokes flow
  Pratelli, A.; Leugering, G. (Eds.): New Trends in Shape Optimization, ISNM 166, 103-115 (2015), Springer International Publishing
  doi.org/10.1007/978-3-319-17563-8_5
  (with Claudia Hecht)
  PREPRINT
   
• Multi-material phase field approach to structural topology optimization
  Leugering, G.; Benner, P; Engell, S.; Griewank, A.; Harbrecht, H.; Hinze, M.; Rannacher and Ulbrich, S.(Eds.): Trends in PDE Optimization, ISNM 165, 231-246 (2014), Birkhäuser Verlag
  doi.org/10.1007/978-3-319-05083-6_15
  (with Luise Blank, Hassan Farshbaf-Shaker, Christoph Rupprecht, Vanessa Styles)
  PREPRINT
   
• Allen-Cahn and Cahn-Hilliard variational inequalities solved with optimization techniques
  Leugering, G.; Engell, S.; Griewank, A.; Hinze, M.; Rannacher, R.; Schulz, V.; Ulbrich, M.; Ulbrich, S.(Eds.): International Series of Numerical Mathematics, Vol. 160, 21-35 (2012),
  Constrained Optimization and Optimal Control for Partial Differential Equations, Springer Verlag Basel
  doi.org/10.1007/978-3-0348-0133-1_2
  (with Luise Blank, Martin Butz, Lavinia Sarbu, Vanessa Styles)
  PREPRINT
   
• Phase-field approaches to structural topology optimization
  Leugering, G.; Engell, S.; Griewank, A.; Hinze, M.; Rannacher, R.; Schulz, V.; Ulbrich, M.; Ulbrich, S.(Eds.): International Series of Numerical Mathematics, Vol. 160, 245-255 (2012) Constrained Optimization and Optimal Control for Partial Differential Equations, Springer Verlag Basel
  doi.org/10.1007/978-3-0348-0133-1_13
  (with Luise Blank, Lavinia Sarbu, Tarin Srisupattarawanit, Vanessa Styles, Axel Voigt)
  PREPRINT
   
• Spinodal decomposition in the presence of elastic interactions
  A reprint from: S.Hildebrand/H.Karcher (Eds.), Geometric Analysis and Nonlinear Partial Differential Equations, Springer Verlag (2003),
  doi.org/10.1007/978-3-642-55627-2_32
  (with. S. Maier-Paape and U. Weikard)
  PREPRINT
   
• Multiple scales in phase separating systems with elastic misfit
  Contribution in Analysis, Modeling and Simulation of Multiscale Problems, A. Mielke (ed.) Springer-Verlag, Berlin, 153-178, (2006),
  doi.org/10.1007/3-540-35657-6_6
  (with Martin Lenz, Barbara Niethammer, Martin Rumpf, and Ulrich Weikard)
  PREPRINT
   
• On asymptotic limits of Cahn-Hilliard systems with elastic misfit
  Contribution in Analysis, Modeling and Simulation of Multiscale Problems, A. Mielke (ed.) Springer-Verlag, Berlin, 87-112, (2006),
  doi.org/10.1007/3-540-35657-6_4
  (with David Jung Chul Kwak)
  PREPRINT
   
• Multiscale Problems in Solidification Processes
  Contribution in Analysis, Modeling and Simulation of Multiscale Problems, A. Mielke (ed.) Springer-Verlag, Berlin, 21-64, (2006),
  doi.org/10.1007/3-540-35657-6_2
  (with Christof Eck and Björn Stinner)
   
• Modelling of non-isothermal multi-component, multi-phase systems with convection
  Phase Transformations in Multicomponent Melts. Wiley-VCH Verlag, Weinheim 325-338 (2008)
  (with Robert Haas)
  PREPRINT

in proceedings:

• Stability analysis of stationary solutions for surface diffusion flow equation
  Proceedings of the Conference ``Pattern formation and asymptotic geometric structure in reaction-diffusion systems'', October 2003 Kyoto.
  Surikaisekikenkyusho Kokyuroku No. 1356, 27-43. (2004),
  (with K. Ito and Y. Kohsaka)
  PREPRINT
   
• Multi-phase-field model for the motion of multiple interfaces
  Proceedings of the ReX&GG Conference Aachen Germany (2001),
  eds. G. Gottstein and D.A. Molodov, Springer Verlag
  (with B. Nestler)
  PREPRINT
   
• A Continuous Clustering Method for Vector Fields
  Proceedings IEEE Visualization (2000),
  (with T. Preußer, M. Rumpf, A. Telea, U. Weikard and J. van Wijk)
  PREPRINT
   
• Phase boundaries in alloys with elastic misfit
  In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 202. Birkhäuser, Basel (2001),
  doi.org/10.1007/978-3-0348-8266-8_24
  PREPRINT
   
• On the Cahn-Hilliard equation with non-constant mobility and its asymptotic limit
  in: D. Bainov, A. Dishliev (Eds): Proceedings of the ``Fifth International Colloquium on Differential Equations'' Plovdiv, Bulgaria, SCT Publishing (1994),
  PREPRINT

preprints (not submitted):

• Thermodynamically consistent diffuse interface models for incompressible two-phase flows with different densities
  (2012)
  (with Helmut Abels and Günter Grün)

Habilitation thesis:

• On mathematical models for phase separation in elastically stressed solids
  University Bonn, 2000 (accepted)

PhD thesis:

• Travelling-Wave-Lösungen als Realisierung von Phasenübergängen bei Gedächtnismetallen
  Bonner Mathematische Schriften No. 256, (1993).

Diploma thesis:

• Konstruktion von Lösungen zu Riemannproblemen in zwei Raumdimensionen
  University Bonn, 1989.

Other publications:

• Wie mathematische Modelle helfen, das Wachstum von Tumoren zu verstehen.
  Mitt. Dtsch. Math.-Ver. 29 (2) (2021), 62-67
   
• Kepler, Kristalle und Computer. Mathematik und numerische Simulationen helfen Kristallwachstum zu verstehen.
  Mitt. Dtsch. Math.-Ver. 20 (4) (2012), 219-228
   
• Wer rechnet besser: Mensch oder Computer?
  Beitrag zur Kinderuni 2008