Harald Garcke | Academic Influence

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Harald Garcke

Mathematics

#4578

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#6480

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Measure Theory

#2558

World Rank

#3067

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Mathematics

Harald Garcke's Degrees

PhD Mathematics University of Bonn

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According to Wikipedia, Harald Garcke is a German mathematician and professor at the University of Regensburg. Career and important results Garcke studied Mathematics and Computer Science at the University of Bonn and finished his PhD 1993 as a student of Hans Wilhelm Alt . 1993/94 he was post-doc with Charles M. Elliott at the University of Sussex and from 1994 he was scientific assistant in Bonn where he finished his habilitation in 2000 . In the year 2001 he got offers for professur-positions at the Universities Regensburg and Duisburg. Since 2002 he is full professor at the University of Regensburg where he was dean of the Mathematics department from 2005 to 2007.

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Harald Garcke's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

On the Cahn-Hilliard equation with degenerate mobility (1996) (479)
Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities (2011) (356)
Multicomponent alloy solidification: phase-field modeling and simulations. (2005) (282)
Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility (1999) (224)
A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions (1999) (209)
On A Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, And Qualitativ (1998) (175)
On anisotropic order parameter models for multi-phase system and their sharp interface limits (1998) (164)
A parametric finite element method for fourth order geometric evolution equations (2007) (149)
A Diffuse Interface Model for Alloys with Multiple Components and Phases (2004) (131)
A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport (2015) (125)
On the parametric finite element approximation of evolving hypersurfaces in R3 (2008) (120)
Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations (2008) (109)
The thin viscous flow equation in higher space dimensions (1998) (96)
A multiphase Cahn--Hilliard--Darcy model for tumour growth with necrosis (2017) (92)
On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations (2007) (90)
Well-posedness of a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport (2015) (88)
A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes (2015) (87)
On Cahn—Hilliard systems with elasticity (2003) (86)
On Fully Practical Finite Element Approximations of Degenerate Cahn-Hilliard Systems (2001) (85)
Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities (2011) (84)
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix (1997) (79)
A singular limit for a system of degenerate Cahn-Hilliard equations (2000) (77)
Finite element approximation of a fourth order nonlinear degenerate parabolic equation (1998) (75)
On an Incompressible Navier-Stokes/Cahn-Hilliard System with Degenerate Mobility (2012) (74)
Phase-field Approaches to Structural Topology Optimization (2012) (73)
Analysis of a Cahn--Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis (2016) (67)
Optimal Control of Treatment Time in a Diffuse Interface Model of Tumor Growth (2016) (66)
A phase-field approach for wetting phenomena of multiphase droplets on solid surfaces. (2014) (64)
Phase-field model for multiphase systems with preserved volume fractions. (2008) (63)
Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy system modelling tumour growth (2016) (62)
The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute (2011) (61)
Surfactant Spreading on Thin Viscous Films: Nonnegative Solutions of A Coupled Degenerate System (2006) (58)
ON MATHEMATICAL MODELS FOR PHASE SEPARATION IN ELASTICALLY STRESSED SOLIDS (2007) (58)
Relating phase field and sharp interface approaches to structural topology optimization (2013) (56)
A multi-phase Mullins–Sekerka system: matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem (1998) (56)
A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow (2014) (56)
Numerical computations of faceted pattern formation in snow crystal growth. (2012) (55)
Diffuse interface modelling of soluble surfactants in two-phase flow (2013) (54)
Second order phase field asymptotics for multi-component systems (2006) (52)
A variational formulation of anisotropic geometric evolution equations in higher dimensions (2008) (52)
Allen-Cahn systems with volume constraints (2008) (51)
On a Cahn-Hilliard model for phase separation with elastic misfit (2005) (51)
The Cahn-Hilliard equation with elasticity-finite element approximation and qualitative studies (2001) (51)
Numerical approximation of anisotropic geometric evolution equations in the plane (2007) (50)
Numerical Approximation of Phase Field Based Shape and Topology Optimization for Fluids (2014) (49)
Analysis of a Cahn–Hilliard–Brinkman model for tumour growth with chemotaxis (2018) (48)
On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth (2010) (48)
A Phase Field Model for Continuous Clustering on Vector Fields (2001) (48)
Anisotropy in multi-phase systems: a phase field approach (1999) (47)
Curvature Driven Interface Evolution (2013) (46)
Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves (2012) (45)
Numerical approximation of gradient flows for closed curves in Rd (2010) (45)
Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints (2010) (44)
A stable numerical method for the dynamics of fluidic membranes (2016) (43)
Parametric finite element approximations of curvature-driven interface evolutions (2019) (41)
Parametric Approximation of Surface Clusters driven by Isotropic and Anisotropic Surface Energies (2010) (39)
Weak Solutions of the Cahn-Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach (2018) (37)
A continuous clustering method for vector fields (2000) (37)
On a Cahn–Hilliard–Darcy System for Tumour Growth with Solution Dependent Source Terms (2016) (36)
Transient coarsening behaviour in the Cahn–Hilliard model (2003) (35)
A Stable Parametric Finite Element Discretization of Two-Phase Navier–Stokes Flow (2013) (35)
Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow (2013) (34)
Numerical computations of the dynamics of fluidic membranes and vesicles. (2015) (33)
Finite Element Approximation of Surfactant Spreading on a Thin Film (2003) (31)
ON THE STABLE NUMERICAL APPROXIMATION OF TWO-PHASE FLOW WITH INSOLUBLE SURFACTANT (2013) (31)
Linearized Stability Analysis of Stationary Solutions for Surface Diffusion with Boundary Conditions (2005) (30)
On a Cahn-Hilliard-Brinkman Model for Tumor Growth and Its Singular Limits (2018) (30)
Sharp Interface Limit for a Phase Field Model in Structural Optimization (2014) (28)
Numerical approximation of the Cahn-Larché equation (2005) (28)
Nonlocal Allen–Cahn systems: analysis and a primal–dual active set method (2013) (28)
A Hele–Shaw–Cahn–Hilliard Model for Incompressible Two-Phase Flows with Different Densities (2017) (27)
Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering (2010) (27)
Thermodynamically Consistent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities (2010) (27)
Stable phase field approximations of anisotropic solidification (2012) (26)
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method (2011) (26)
Mechanical Effects in the Cahn-Hilliard Model: A Review on Mathematical Results (2005) (26)
Multi-material phase field approach to structural topology optimization (2013) (26)
A mathematical model for grain growth in thin metallic films (2000) (25)
A phase field model for the electromigration of intergranular voids (2007) (25)
Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid (2005) (24)
A phase field approach to shape optimization in Navier–Stokes flow with integral state constraints (2017) (24)
On a phase field model of Cahn–Hilliard type for tumour growth with mechanical effects (2019) (23)
Solutions of a fourth order degenerate parabolic equation with weak initial trace (1999) (23)
Mean Curvature Flow with Triple Junctions in Higher Space Dimensions (2012) (23)
ELASTIC FLOW WITH JUNCTIONS: VARIATIONAL APPROXIMATION AND APPLICATIONS TO NONLINEAR SPLINES (2012) (22)
Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes (2016) (21)
Finite Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs--Thomson Law (2012) (21)
Modelling of microstructure formation and interface dynamics (2003) (21)
Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques (2012) (20)
Willmore flow of planar networks (2017) (20)
Finite element methods for fourth order axisymmetric geometric evolution equations (2018) (20)
Stable finite element approximations of two-phase flow with soluble surfactant (2015) (19)
On the stable discretization of strongly anisotropic phase field models with applications to crystal growth (2012) (19)
Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen–Cahn equation (2009) (19)
Efficient Image Segmentation and Restoration Using Parametric Curve Evolution with Junctions and Topology Changes (2014) (18)
Bi-directional diffusion induced grain boundary motion with triple junctions (2004) (18)
Shape and Topology Optimization in Stokes Flow with a Phase Field Approach (2016) (18)
On Asymptotic Limits of Cahn-Hilliard Systems with Elastic Misfit (2006) (17)
Surface diffusion with triple junctions: A stability criterion for stationary solutions (2010) (17)
Nonlinear stability of stationary solutions for curvature flow with triple junction (2008) (15)
Variational discretization of axisymmetric curvature flows (2018) (15)
Traveling Wave Solutions as Dynamic Phase Transitions in Shape Memory Alloys (1995) (15)
Linearized stability analysis of surface diffusion for hypersurfaces with triple lines (2013) (15)
Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes (2015) (14)
Weak Solutions and Diffuse Interface Models for Incompressible Two-Phase Flows (2015) (14)
Finite element approximation for the dynamics of asymmetric fluidic biomembranes (2016) (14)
Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law (2011) (14)
A volume-of-fluid method for three-dimensional hexagonal solidification processes (2017) (14)
The ¡-limit of the Ginzburg-Landau energy in an elastic medium (2008) (14)
Nonlinear Stability of Stationary Solutions for Surface Diffusion with Boundary Conditions (2008) (14)
Long time existence of solutions to an elastic flow of networks (2019) (13)
Shape optimization for surface functionals in Navier--Stokes flow using a phase field approach (2015) (13)
On sharp interface limits of Allen--Cahn/Cahn--Hilliard variational inequalities (2007) (13)
Computational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity Effects (2016) (13)
Exponential stability for a mirror–symmetric three phase boundary motion by surface diffusion (2003) (13)
Optimal control of time-discrete two-phase flow driven by a diffuse-interface model (2016) (12)
Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow (2014) (11)
Stable numerical approximation of two-phase flow with a Boussinesq-Scriven surface fluid (2014) (11)
Stress- and diffusion-induced interface motion: Modelling and numerical simulations (2007) (11)
Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation (2017) (11)
Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature (2017) (10)
Sparse Optimal Control of a Phase Field Tumor Model with Mechanical Effects (2020) (10)
Image Segmentation Using Parametric Contours With Free Endpoints (2015) (10)
Phase Field Models versus Parametric Front Tracking Methods: Are they accurate and computationally efficient? (2012) (10)
Stability of Spherical Caps under the Volume-Preserving Mean Curvature Flow with Line Tension (2014) (9)
Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biomembranes (2010) (9)
Cahn-Hilliard inpainting with the double obstacle potential (2018) (8)
Mathematik Primal-dual active set methods for Allen-Cahn variational inequalities with non-local constraints (2009) (8)
Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants (2017) (8)
Cahn–Hilliard–Brinkman systems for tumour growth (2020) (8)
A Phase Field Approach for Shape and Topology Optimization in Stokes Flow (2015) (8)
Local well‐posedness for volume‐preserving mean curvature and Willmore flows with line tension (2013) (8)
Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach (2020) (8)
Numerical approximation of curve evolutions in Riemannian manifolds (2018) (8)
Two-Phase Flow with Surfactants: Diffuse Interface Models and Their Analysis (2016) (7)
Modeling of Nonisothermal Multi‐Component, Multi‐Phase Systems with Convection (2009) (7)
Volume-Preserving Parametric Finite Element Methods for Axisymmetric Geometric Evolution Equations (2021) (7)
Short time existence for coupling of scaled mean curvature flow and diffusion (2022) (6)
Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces (2022) (6)
Stable approximations for axisymmetric Willmore flow for closed and open surfaces (2019) (6)
Stability analysis for stationary solutions of the Mullins–Sekerka flow with boundary contact (2019) (6)
Stable Discretizations of Elastic Flow in Riemannian Manifolds (2018) (6)
An anisotropic, inhomogeneous, elastically modified Gibbs–Thomson law as singular limit of a diffuse interface model (2009) (6)
Spinodal Decomposition in the Presence of Elastic Interactions (2003) (6)
Learning patient‐specific parameters for a diffuse interface glioblastoma model from neuroimaging data (2019) (5)
Long-time dynamics of the Cahn–Hilliard equation with kinetic rate dependent dynamic boundary conditions (2021) (5)
On the Surface Diffusion Flow with Triple Junctions in Higher Space Dimensions (2019) (5)
On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions (2014) (5)
Analysis of Cahn‐Hilliard‐Brinkman models for tumour growth (2019) (5)
Qualitative properties for a system coupling scaled mean curvature flow and diffusion (2022) (5)
A Phase-field Model for the Solidification Process in Multicomponent Alloys (2003) (4)
Multiscale Problems in Solidification Processes (2006) (4)
Viscoelastic Cahn-Hilliard models for tumour growth (2022) (4)
Mini-Workshop: Mathematics of Biological Membranes (2008) (4)
Long-time dynamics for a Cahn–Hilliard tumor growth model with chemotaxis (2020) (4)
Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes (2015) (4)
Erratum: Numerical computations of the dynamics of fluidic membranes and vesicles [Phys. Rev. E 92, 052704 (2015)]. (2016) (4)
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids (2021) (4)
Overhang Penalization in Additive Manufacturing via Phase Field Structural Topology Optimization with Anisotropic Energies (2021) (4)
Weak Solutions and Diffuse Interface Models for IncompressibleTwo-Phase Flows (2018) (3)
Stability analysis of phase boundary motion by surface diffusion with triple junction (2009) (3)
Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds (2020) (3)
Non-linear stability of double bubbles under surface diffusion (2019) (3)
Universität Regensburg Mathematik Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biological membranes (2009) (3)
A Cahn-Hilliard model coupled to viscoelasticity with large deformations (2022) (3)
A Diffuse Interface Model for Cell Blebbing Including Membrane-Cortex Coupling with Linker Dynamics (2021) (3)
Phase-field methods for spectral shape and topology optimization (2021) (3)
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters (2022) (3)
Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes (2020) (3)
Standard Planar Double Bubbles are Stable under Surface Diffusion Flow (2015) (3)
Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities (2022) (2)
Optimal control of time discrete two‐phase flow governed by a diffuse interface model (2016) (2)
An inhomogeneous, anisotropic, elastically modified GibbsThomson law as singular limit of a diffuse interface model (2010) (2)
Numerical analysis for a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport (2021) (2)
Standard planar double bubbles are dynamically stable under surface diffusion flow (2021) (2)
On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces (2019) (2)
Numerical Approximation of Anisotropic Geometric Evolution Equations (2006) (2)
Multiple Scales in Phase Separating Systems with Elastic Misfit (2006) (2)
Image Segmentation and Restoration Using Parametric Contours With Free Endpoints (2015) (1)
Structure-preserving discretizations of two-phase Navier-Stokes flow using fitted and unfitted approaches (2022) (1)
Eliminating spurious velocities with a stable approximation of incompressible two-phase flow (2013) (1)
Universität Regensburg Mathematik Numerical computations of facetted pattern formation in snow crystal growth (2012) (1)
Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities (2012) (1)
Mathematik Eliminating spurious velocities with a stable approximation of incompressible two-phase flow (2013) (1)
A Hele–Shaw–Cahn–Hilliard Model for Incompressible Two-Phase Flows with Different Densities (2017) (1)
Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations (2022) (1)
Diffuse Interface Approaches in Atmosphere and Ocean—Modeling and Numerical Implementation (2016) (1)
On the Cahn { Hilliard equation with non { constantmobility and its asymptotic limitHarald (2007) (1)
Shape and Topology Optimization in Stokes Flow with a Phase Field Approach (2015) (0)
Sharp interface analysis of a diffuse interface model for cell blebbing with linker dynamics (2023) (0)
Nonlinear Evolution Equations : Analysis and Numerics 783 Workshop : Nonlinear Evolution Equations : Analysis and Numerics Table of Contents (2015) (0)
Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes (2017) (0)
Curvature Driven Interface Evolution (2013) (0)
A P ] 3 0 N ov 2 01 7 Willmore flow of planar networks (2018) (0)
Mini-Workshop Mathematics of Biological Membranes (Oberwolfach, Germany, August 31-September 6, 2008) (2008) (0)
Mathematical Models and Methods in Applied Sciences F a Mathematical Model for Grain Growth in Thin Metallic Films (2007) (0)
PARAMETRISED SIMPLICIAL VOLUME (2019) (0)
Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures (2023) (0)
Multi-phase-field model for the motion of multiple interfaces (2001) (0)
Partial Differential Equations (2017) (0)
Phase field topology optimisation for 4D printing (2022) (0)
Universität Regensburg Mathematik Diffuse interface modelling of soluble surfactants in two-phase flow (2013) (0)
Mathematik Multiscale Problems in Solidification Processes (2006) (0)
Regensburg Mathematik Allen-Cahn systems with volume constraints (2007) (0)
Universität Regensburg Mathematik Allan-Cahn and Cahn-Hilliard variational inequalities solved with Optimization Techniques (2010) (0)
Stability analysis of stationary solutions for surface diffusion flow equation (Pattern formation and asymptotic geometric structure in reaction-diffusion systems) (2004) (0)
Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes (2015) (0)
Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures (2020) (0)
Acknowledgements of reviewers 2018 (2019) (0)
Finite element approximation of a sharp interface approach for gradient flow dynamics of two-phase biomembranes (2017) (0)
On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions (2015) (0)
A stable numerical method for the dynamics of fluidic membranes (2016) (0)
Universität Regensburg Mathematik Elastic flow with junctions : Variational approximation and application to nonlinear splines (2011) (0)
Optimal Control of Treatment Time in a Diffuse Interface Model of Tumor Growth (2017) (0)
Mathematik Existence of weak solutions for the Stefan problem with anisotropic (2011) (0)
Variational discretization of axisymmetric curvature flows (2019) (0)
Systems of Linear Equations (2017) (0)
Phase Boundaries in Alloys with Elastic Misfit (2001) (0)
Long-time dynamics for a Cahn–Hilliard tumor growth model with chemotaxis (2020) (0)
Basic Principles of Thermodynamics (2017) (0)
Mean Curvature Flow with Triple Junctions in Higher Space Dimensions (2013) (0)
Ordinary Differential Equations (2017) (0)
Phase-field modelling of grain growth (2001) (0)
Universität Regensburg Mathematik Image segmentaion and restoration using parametric contours with free endpoints (2015) (0)
Unfitted finite element methods for axisymmetric two-phase flow (2023) (0)
A Stable Parametric Finite Element Discretization of Two-Phase Navier–Stokes Flow (2014) (0)
A Diffuse-Interface Approach for Solid-State Dewetting with Anisotropic Surface Energies (2022) (0)
A phase field approach to shape optimization in Navier–Stokes flow with integral state constraints (2018) (0)
A Phase-Field Approach to Shape and Topology Optimization of Acoustic Waves in Dissipative Media (2021) (0)
On the Cahn { Hilliard equation withdegenerate mobilityCharles (1996) (0)
On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces (2020) (0)
A Cahn-Hilliard phase field model coupled to an Allen-Cahn model of viscoelasticity at large strains (2023) (0)
Fast image segmentation and restoration using parametric curve evolution with junctions and topology changes (2013) (0)
On a Cahn–Hilliard model for phase separation with elastic m Sur un modèle de Cahn–Hilliard pour la phase de séparation misfit élastique (2005) (0)
Free Boundary Problems (2017) (0)
Willmore Flow of Networks (2018) (0)
Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves (2011) (0)
A P ] 1 6 N ov 2 01 8 On a Cahn-Hilliard-Brinkman model for tumour growth and its singular limits (2018) (0)

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