Research Harald Garcke

recent preprints:

• 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 modelling protocells (2025)
  (with Kei Fong Lam, Robert Nürnberg, Andrea Signori)
  
  
• A finite element method for anisotropic crystal growth on surfaces (2024)
  (with Robert Nürnberg)
  

in refereed journals:

• 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: Modelling 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

• 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

• 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
  Numerical Mathematics (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 stabilisation for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities (2024)
  Mathematical Annals (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: Modelling 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
  Numerical Mathematics (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 stabilisation for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities (2024)
  Mathematical Annals (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 optimisation 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 discretisations 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 penalisation in additive manufacturing via phase field structural topology optimization with anisotropic energies
  Applied Mathematics & Optimisation 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 optimisation
  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 optimisation of acoustic waves in dissipative media
  SIAM Journal on Control and Optimisation 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
  Numerical Mathematics 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
  Mathematical News, 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 optimisation 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 tumour 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 discretisations 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 discretisation of axisymmetric curvature flows
  Numerical Mathematics 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 optimisation 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 modelling 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 tumour 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 optimisation
  SIAM J. Control Optim. 54 (3), 1558-1548 (2016),
  doi.org/10.1137/140989066
  (with Luise Blank, Claudia Hecht and Christoph Rupprecht)
  PREPRINT
  
• Shape optimisation 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 modelling 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
  Numerical Mathematics 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 & Optimisation 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 discretisation 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 optimisation 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 optimisation 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 discretisation 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 optimisation
  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
  Annual Report of the German Mathematical Society, 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 discretisation 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
  
• Linearised 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 ^ℝd
  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 Centre 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, Numerical Mathematics 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
  
• Linearised 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
  Mathematics News 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 Visualisation 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 systems: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-phase systems 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 discretisation 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 multicomponent systems 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 - modelling 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 optimisation in Stokes flow
  Pratelli, A.; Leugering, G. (Eds.): New Trends in Shape Optimisation, 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 optimisation
  Leugering, G.; Benner, P; Engell, S.; Griewank, A.; Harbrecht, H.; Hinze, M.; Rannacher and Ulbrich, S.(Eds.): Trends in PDE Optimisation, 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 optimisation 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 Optimisation 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 optimisation
  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 Optimisation 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, Modelling 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, Modelling 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, Modelling 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 Publishers, 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 Visualisation (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 solutions as realisation of phase transitions in memory metals
  Bonner Mathematische Schriften No. 256, (1993).

Diploma thesis:

• Construction of solutions to Riemann problems in two space dimensions
  University of Bonn, 1989.

Other publications:

• How mathematicians help to understand the growth of tumours.
  Mitt. Dtsch. Math. 29 (2) (2021), 62-67
  
• Kepler, crystals and computers. Mathematics and numerical simulations help to understand crystal growth.
  Mitt. Dtsch. Math. 20 (4) (2012), 219-228
  
• Who does maths better: humans or computers?
  Contribution to the Children's University 2008