Finite element approximation of a fourth order nonlinear degenerate parabolic equation. - John W. Barrett 001; James F. Blowey; Harald Garcke (Numerische Mathematik, 1998)

A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions. - Harald Garcke; Britta Nestler; Barbara Stoth (SIAM J. Appl. Math., 1999)

Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility. - John W. Barrett 001; James F. Blowey; Harald Garcke (SIAM J. Numer. Anal., 1999)

A continuous clustering method for vector fields. - Harald Garcke; Tobias Preußer; Martin Rumpf; Alexandru C. Telea; Ulrich Weikard; Jarke J. van Wijk (IEEE Visualization, 2000)

A Phase Field Model for Continuous Clustering on Vector Fields. - Harald Garcke; Tobias Preußer; Martin Rumpf; Alexandru C. Telea; Ulrich Weikard; Jarke J. van Wijk (IEEE Trans. Vis. Comput. Graph., 2001)

Finite Element Approximation of Surfactant Spreading on a Thin Film. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (SIAM J. Numer. Anal., 2003)

A Diffuse Interface Model for Alloys with Multiple Components and Phases. - Björn Stinner; Britta Nestler; Harald Garcke (SIAM J. Appl. Math., 2004)

Numerical approximation of the Cahn-Larché equation. - Harald Garcke; Ulrich Weikard (Numerische Mathematik, 2005)

Linearized Stability Analysis of Stationary Solutions for Surface Diffusion with Boundary Conditions. - Harald Garcke; Kazuo Ito; Yoshihito Kohsaka (SIAM J. Math. Anal., 2005)

Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (Math. Comput., 2006)

Surfactant Spreading on Thin Viscous Films: Nonnegative Solutions of A Coupled Degenerate System. - Harald Garcke; Sandra Wieland (SIAM J. Math. Anal., 2006)

A parametric finite element method for fourth order geometric evolution equations. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (J. Comput. Phys., 2007)

On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (SIAM J. Sci. Comput., 2007)

On the parametric finite element approximation of evolving hypersurfaces in R3. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (J. Comput. Phys., 2008)

A variational formulation of anisotropic geometric evolution equations in higher dimensions. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (Numerische Mathematik, 2008)

Nonlinear Stability of Stationary Solutions for Surface Diffusion with Boundary Conditions. - Harald Garcke; Kazuo Ito; Yoshihito Kohsaka (SIAM J. Math. Anal., 2008)

Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (SIAM J. Sci. Comput., 2008)

On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (J. Comput. Phys., 2010)

Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques. - Luise Blank; Martin Butz; Harald Garcke; Lavinia Sarbu; Vanessa Styles (Constrained Optimization and Optimal Control for Partial Differential Equations, 2012)

Phase-field Approaches to Structural Topology Optimization. - Luise Blank; Harald Garcke; Lavinia Sarbu; Tarin Srisupattarawanit; Vanessa Styles; Axel Voigt (Constrained Optimization and Optimal Control for Partial Differential Equations, 2012)

Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (Numerische Mathematik, 2012)

Fast image segmentation and restoration using parametric curve evolution with junctions and topology changes. - Heike Benninghoff; Harald Garcke (CoRR, 2013)

Efficient Image Segmentation and Restoration Using Parametric Curve Evolution with Junctions and Topology Changes. - Heike Benninghoff; Harald Garcke (SIAM J. Imaging Sci., 2014)

Image Segmentation and Restoration Using Parametric Contours With Free Endpoints. - Heike Benninghoff; Harald Garcke (CoRR, 2015)

Stable finite element approximations of two-phase flow with soluble surfactant. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (J. Comput. Phys., 2015)

A Stable Parametric Finite Element Discretization of Two-Phase Navier-Stokes Flow. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (J. Sci. Comput., 2015)

Numerical Approximation of Phase Field Based Shape and Topology Optimization for Fluids. - Harald Garcke; Claudia Hecht; Michael Hinze; Christian Kahle (SIAM J. Sci. Comput., 2015)

Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes. - Heike Benninghoff; Harald Garcke (J. Math. Imaging Vis., 2016)

A stable numerical method for the dynamics of fluidic membranes. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (Numerische Mathematik, 2016)

Sharp Interface Limit for a Phase Field Model in Structural Optimization. - Luise Blank; Harald Garcke; Claudia Hecht; Christoph Rupprecht (SIAM J. Control. Optim., 2016)

Computational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity Effects. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (SIAM J. Numer. Anal., 2016)

Image Segmentation Using Parametric Contours With Free Endpoints. - Heike Benninghoff; Harald Garcke (IEEE Trans. Image Process., 2016)

A volume-of-fluid method for three-dimensional hexagonal solidification processes. - Martin Reitzle; Corine Kieffer-Roth; Harald Garcke; Bernhard Weigand (J. Comput. Phys., 2017)

Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes. - Heike Benninghoff; Harald Garcke (J. Sci. Comput., 2017)

Finite element approximation for the dynamics of asymmetric fluidic biomembranes. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (Math. Comput., 2017)

A phase field approach to shape optimization in Navier-Stokes flow with integral state constraints. - Harald Garcke; Michael Hinze; Christian Kahle; Kei Fong Lam (Adv. Comput. Math., 2018)

Cahn-Hilliard Inpainting with the Double Obstacle Potential. - Harald Garcke; Kei Fong Lam; Vanessa Styles (SIAM J. Imaging Sci., 2018)

Stable approximations for axisymmetric Willmore flow for closed and open surfaces. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (CoRR, 2019)

Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data. - Abramo Agosti; Pasquale Ciarletta; Harald Garcke; Michael Hinze (CoRR, 2019)

Finite element methods for fourth order axisymmetric geometric evolution equations. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (J. Comput. Phys., 2019)

Variational discretization of axisymmetric curvature flows. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (Numerische Mathematik, 2019)

On a Cahn-Hilliard-Brinkman Model for Tumor Growth and Its Singular Limits. - Matthias Ebenbeck; Harald Garcke (SIAM J. Math. Anal., 2019)

Stable Discretizations of Elastic Flow in Riemannian Manifolds. - John W. Barrett 001; Harald Garcke; Robert Nürnberg (SIAM J. Numer. Anal., 2019)

Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes. - Harald Garcke; Robert Nürnberg (CoRR, 2020)

Weak Solutions of the Cahn-Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach. - Harald Garcke; Patrik Knopf (SIAM J. Math. Anal., 2020)

Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds. - Harald Garcke; Robert Nürnberg (Numerische Mathematik, 2021)

Sparse Optimal Control of a Phase Field Tumor Model with Mechanical Effects. - Harald Garcke; Kei Fong Lam; Andrea Signori (SIAM J. Control. Optim., 2021)

A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters. - Weizhu Bao; Harald Garcke; Robert Nürnberg; Quan Zhao (CoRR, 2022)

Viscoelastic Cahn-Hilliard models for tumour growth. - Harald Garcke; Balázs Kovács; Dennis Trautwein (CoRR, 2022)

Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations. - Weizhu Bao; Harald Garcke; Robert Nürnberg; Quan Zhao (J. Comput. Phys., 2022)

Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. - Harald Garcke; Dennis Trautwein (J. Num. Math., 2022)

Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. - Charles M. Elliott; Harald Garcke; Balázs Kovács (Numerische Mathematik, 2022)

A Diffuse Interface Model for Cell Blebbing Including Membrane-Cortex Coupling with Linker Dynamics. - Philipp Werner; Martin Burger 001; Florian Frank; Harald Garcke (SIAM J. Appl. Math., 2022)

A Phase-Field Approach to Shape and Topology Optimization of Acoustic Waves in Dissipative Media. - Harald Garcke; Sourav Mitra; Vanja Nikolic (SIAM J. Control. Optim., 2022)

A Cahn-Hilliard phase field model coupled to an Allen-Cahn model of viscoelasticity at large strains. - Abramo Agosti; Pierluigi Colli; Harald Garcke; Elisabetta Rocca (CoRR, 2023)

Approximation and existence of a viscoelastic phase-field model for tumour growth in two and three dimensions. - Harald Garcke; Dennis Trautwein (CoRR, 2023)

Structure-preserving discretizations of two-phase Navier-Stokes flow using fitted and unfitted approaches. - Harald Garcke; Robert Nürnberg; Quan Zhao (J. Comput. Phys., 2023)

A Diffuse-Interface Approach for Solid-State Dewetting with Anisotropic Surface Energies. - Harald Garcke; Patrik Knopf; Robert Nürnberg; Quan Zhao (J. Nonlinear Sci., 2023)

Unfitted Finite Element Methods for Axisymmetric Two-Phase Flow. - Harald Garcke; Robert Nürnberg; Quan Zhao (J. Sci. Comput., 2023)

A finite element method for anisotropic crystal growth on surfaces. - Harald Garcke; Robert Nürnberg (CoRR, 2024)

Parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. - Harald Garcke; Robert Nürnberg; Dennis Trautwein (CoRR, 2024)

A variational front-tracking method for multiphase flow with triple junctions. - Harald Garcke; Robert Nürnberg; Quan Zhao (CoRR, 2024)

Structure-preserving parametric finite element method for curve diffusion based on Lagrange multiplier approaches. - Harald Garcke; Wei Jiang 008; Chunmei Su; Ganghui Zhang (CoRR, 2024)

Arbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flow. - Harald Garcke; Robert Nürnberg; Quan Zhao (Comput. Math. Appl., 2024)

Corrigendum to: Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. - Harald Garcke; Dennis Trautwein (J. Num. Math., 2024)

A structure-preserving finite element method for the multi-phase Mullins-Sekerka problem with triple junctions. - Tokuhiro Eto; Harald Garcke; Robert Nürnberg (Numerische Mathematik, 2024)

Isoparametric finite element methods for mean curvature flow and surface diffusion. - Harald Garcke; Robert Nürnberg; Simon Praetorius; Ganghui Zhang (J. Comput. Phys., 2025)

Structure-Preserving Parametric Finite Element Method for Surface Diffusion Based on Lagrange Multiplier Approaches. - Harald Garcke; Wei Jiang 008; Chunmei Su; Ganghui Zhang (SIAM J. Sci. Comput., 2025)

Stable fully discrete finite element methods with BGN tangential motion for Willmore flow of planar curves. - Harald Garcke; Robert Nürnberg; Quan Zhao (CoRR, 2025)

An energy-stable minimal deformation rate scheme for mean curvature flow and surface diffusion. - Guangwei Gao; Harald Garcke; Buyang Li; Rong Tang (CoRR, 2025)

Stable fully practical finite element methods for axisymmetric Willmore flow. - Harald Garcke; Robert Nürnberg; Quan Zhao (CoRR, 2025)

A parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions. - Tokuhiro Eto; Harald Garcke; Robert Nürnberg (CoRR, 2025)

An energy-stable parametric finite element method for Willmore flow with normal-tangential velocity splitting. - Harald Garcke; Robert Nürnberg; Quan Zhao (CoRR, 2025)

Error estimates for a surface finite element method for anisotropic mean curvature flow. - Klaus Deckelnick; Harald Garcke; Balázs Kovács (CoRR, 2025)

Structure-preserving parametric finite element methods for two-phase Stokes flow based on Lagrange multiplier approaches. - Harald Garcke; Dennis Trautwein; Ganghui Zhang (CoRR, 2025)