Edit Profile (opens in new tab) Garcke, Harald Compute Distance To: Compute Author ID: garcke.harald Published as: Garcke, Harald; Garcke, H. External Links: MGP · Wikidata · GND Documents Indexed: 153 Publications since 1993, including 5 Books 2 Contributions as Editor Co-Authors: 72 Co-Authors with 145 Joint Publications 1,379 Co-Co-Authors all top 5 Co-Authors 9 single-authored 44 Nürnberg, Robert 41 Barrett, John W. 15 Lam, Kei Fong 10 Abels, Helmut 10 Styles, Vanessa 8 Blank, Luise 7 Nestler, Britta 6 Hecht, Claudia 6 Hinze, Michael 6 Kohsaka, Yoshihito 6 Stinner, Bjorn 5 Eck, Christof 5 Elliott, Charles M. 5 Ito, Kazuo 5 Kahle, Christian 4 Benninghoff, Heike 4 Depner, Daniel 4 Ebenbeck, Matthias 4 Grün, Günther 4 Knabner, Peter 4 Sarbu, Lavinia 4 Stoth, Barbara E. E. 4 Weikard, Ulrich 3 Blowey, James F. 3 Dal Passo, Roberta 3 Knopf, Patrik 2 Arab, Nasrin 2 Butz, Martin V. 2 Gößwein, M. 2 Menzel, Julia H. 2 Müller, Lars 2 Niethammer, Barbara 2 Pluda, Alessandra 2 Röger, Matthias 2 Rumpf, Martin 2 Rupprecht, Christoph 2 Signori, Andrea 2 Sitka, Emanuel 2 Weber, Josef 2 Yayla, Sema 1 Agosti, Abramo 1 Alfaro, Matthieu 1 Bao, Weizhu 1 Bertsch, Michiel 1 Bronsard, Lia 1 Ciarletta, Pasquale 1 Dede’, Luca 1 Escher, Joachim 1 Hilhorst, Danielle 1 Hüttl, Paul 1 Kampmann, Johannes 1 Kornhuber, Ralf 1 Kraus, Christiane 1 Kwak, David Jung Chul 1 Lenz, Martin 1 Maier-Paape, Stanislaus 1 Matano, Hiroshi 1 Matioc, Bogdan-Vasile 1 Metzger, Stefan 1 Novick-Cohen, Amy 1 Peletier, Mark Adriaan 1 Rätz, Andreas 1 Rocca, Elisabetta 1 Schatzle, Reiner 1 Schaubeck, Stefan 1 Ševčovič, Daniel 1 Srisupattarawanit, Tarin 1 Sturzenhecker, Thomas 1 Voigt, Axel 1 Wendler, Frank 1 Wieland, Sandra 1 Zhao, Quan all top 5 Serials 7 IMA Journal of Numerical Analysis 7 Numerische Mathematik 7 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 SIAM Journal on Mathematical Analysis 7 Interfaces and Free Boundaries 6 Journal of Computational Physics 5 Advances in Mathematical Sciences and Applications 4 Journal of Differential Equations 4 SIAM Journal on Numerical Analysis 4 Advances in Differential Equations 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Physica D 3 European Journal of Applied Mathematics 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 SIAM Journal on Scientific Computing 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Discrete and Continuous Dynamical Systems. Series S 3 Springer-Lehrbuch 2 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 2 Mathematics of Computation 2 Applied Mathematics and Optimization 2 Hokkaido Mathematical Journal 2 Mathematische Nachrichten 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 SIAM Journal on Control and Optimization 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Numerical Methods for Partial Differential Equations 2 Journal of Scientific Computing 2 SIAM Journal on Applied Mathematics 2 Journal of Mathematical Fluid Mechanics 2 Journal of Evolution Equations 2 Communications in Mathematical Sciences 2 Oberwolfach Reports 2 SIAM Journal on Imaging Sciences 1 Archive for Rational Mechanics and Analysis 1 Computer Methods in Applied Mechanics and Engineering 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Numerical Mathematics 1 Communications in Partial Differential Equations 1 Journal of Mathematical Imaging and Vision 1 Communications in Analysis and Geometry 1 Advances in Computational Mathematics 1 Discrete and Continuous Dynamical Systems 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 IEEE Transactions on Image Processing 1 Nonlinear Analysis. Real World Applications 1 Communications on Pure and Applied Analysis 1 Bonner Mathematische Schriften 1 Communications in Computational Physics 1 Advances in Nonlinear Analysis 1 Geometric Flows 1 AIMS Mathematics 1 Springer Undergraduate Mathematics Series 1 SMAI Journal of Computational Mathematics all top 5 Fields 119 Partial differential equations (35-XX) 61 Numerical analysis (65-XX) 42 Fluid mechanics (76-XX) 35 Mechanics of deformable solids (74-XX) 32 Calculus of variations and optimal control; optimization (49-XX) 30 Differential geometry (53-XX) 24 Biology and other natural sciences (92-XX) 21 Classical thermodynamics, heat transfer (80-XX) 20 Statistical mechanics, structure of matter (82-XX) 6 General and overarching topics; collections (00-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Information and communication theory, circuits (94-XX) 4 Ordinary differential equations (34-XX) 3 Operations research, mathematical programming (90-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Computer science (68-XX) 1 Real functions (26-XX) 1 Convex and discrete geometry (52-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 142 Publications have been cited 2,269 times in 1,100 Documents Cited by ▼ Year ▼ On the Cahn-Hilliard equation with degenerate mobility. Zbl 0856.35071Elliott, Charles M.; Garcke, Harald 202 1996 Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Zbl 1242.76342Abels, Helmut; Garcke, Harald; Grün, Günther 146 2012 On a fourth-order degenerate parabolic equation: Global entropy estimates, existence, and qualitative behavior of solutions. Zbl 0929.35061Dal Passo, Roberta; Garcke, Harald; Grün, Günther 95 1998 Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. Zbl 0947.65109Barrett, John W.; Blowey, James F.; Garcke, Harald 85 1999 A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. Zbl 1336.92038Garcke, Harald; Lam, Kei Fong; Sitka, Emanuel; Styles, Vanessa 63 2016 A parametric finite element method for fourth order geometric evolution equations. Zbl 1112.65093Barrett, John W.; Garcke, Harald; Nürnberg, Robert 59 2007 On anisotropic order parameter models for multi-phase systems and their sharp interface limits. Zbl 0936.82010Garcke, Harald; Nestler, Britta; Stoth, Barbara 46 1998 A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis. Zbl 1380.92029Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel 44 2018 On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\). Zbl 1145.65068Barrett, John W.; Garcke, Harald; Nürnberg, Robert 44 2008 A multiphase field concept: Numerical simulations of moving phase boundaries and multiple junctions. Zbl 0942.35095Garcke, Harald; Nestler, Britta; Stoth, Barbara 42 1999 Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. Zbl 1375.92011Garcke, Harald; Lam, Kei Fong 41 2017 The thin viscous flow equation in higher space dimensions. Zbl 0954.35035Bertsch, Michiel; Dal Passo, Roberta; Garcke, Harald; Grün, Günther 40 1998 Parametric approximation of willmore flow and related geometric evolution equations. Zbl 1186.65133Barrett, John W.; Garcke, Harald; Nürnberg, Robert 40 2008 On the variational approximation of combined second and fourth order geometric evolution equations. Zbl 1148.65074Barrett, John W.; Garcke, Harald; Nürnberg, Robert 38 2007 Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities. Zbl 1273.76421Abels, Helmut; Depner, Daniel; Garcke, Harald 36 2013 Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Zbl 0913.65084Barrett, John W.; Blowey, James F.; Garcke, Harald 35 1998 On fully practical finite element approximations of degenerate Cahn-Hilliard systems. Zbl 0987.35071Barrett, John W.; Blowey, James F.; Garcke, Harald 33 2001 On Cahn-Hilliard systems with elasticity. Zbl 1130.74037Garcke, Harald 33 2003 On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. Zbl 1347.76052Abels, Helmut; Depner, Daniel; Garcke, Harald 33 2013 Diffuse interface modelling of soluble surfactants in two-phase flow. Zbl 1319.35309Garcke, Harald; Lam, Kei Fong; Stinner, Björn 30 2014 A singular limit for a system of degenerate Cahn-Hilliard equations. Zbl 0988.35019Garcke, Harald; Novick-Cohen, Amy 29 2000 Optimal control of treatment time in a diffuse interface model of tumor growth. Zbl 1403.35139Garcke, Harald; Lam, Kei Fong; Rocca, Elisabetta 29 2018 Analysis of a Cahn-Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis. Zbl 1360.35042Garcke, Harald; Lam, Kei Fong 29 2017 A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow. Zbl 1329.76168Garcke, Harald; Hinze, Michael; Kahle, Christian 27 2016 Surfactant spreading on thin viscous films: nonnegative solutions of a coupled degenerate system. Zbl 1102.35056Garcke, Harald; Wieland, Sandra 27 2006 Existence results for diffusive surface motion laws. Zbl 0876.35050Elliott, Charles M.; Garcke, Harald 26 1997 Phase-field approaches to structural topology optimization. Zbl 1356.49044Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Srisupattarawanit, Tarin; Styles, Vanessa; Voigt, Axel 24 2012 The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute. Zbl 1218.65105Barrett, John W.; Garcke, Harald; Nürnberg, Robert 24 2011 Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth. Zbl 1434.35255Garcke, Harald; Lam, Kei Fong 24 2016 Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis. Zbl 1410.35058Ebenbeck, Matthias; Garcke, Harald 24 2019 On a Cahn–Hilliard model for phase separation with elastic misfit. Zbl 1072.35081Garcke, Harald 22 2005 A stable numerical method for the dynamics of fluidic membranes. Zbl 1391.76298Barrett, John W.; Garcke, Harald; Nürnberg, Robert 20 2016 Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. Zbl 1242.65188Barrett, John W.; Garcke, Harald; Nürnberg, Robert 18 2012 Relating phase field and sharp interface approaches to structural topology optimization. Zbl 1301.49113Blank, Luise; Garcke, Harald; Farshbaf-Shaker, M. Hassan; Styles, Vanessa 17 2014 Second order phase field asymptotics for multi-component systems. Zbl 1106.35116Garcke, Harald; Stinner, Björn 17 2006 Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints. Zbl 1272.65060Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa 17 2013 Numerical approximation of phase field based shape and topology optimization for fluids. Zbl 1322.35113Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian 17 2015 A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities. Zbl 1394.35353Dedè, Luca; Garcke, Harald; Lam, Kei Fong 16 2018 On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms. Zbl 1406.92296Garcke, Harald; Lam, Kei Fong 16 2018 A multi-phase Mullins-Sekerka system: Matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem. Zbl 0924.35199Bronsard, Lia; Garcke, Harald; Stoth, Barbara 16 1998 The Cahn-Hilliard equation with elasticity – finite element approximation and qualitative studies. Zbl 0972.35164Garcke, Harald; Rumpf, Martin; Weikard, Ulrich 16 2001 Finite element approximation of surfactant spreading on a thin film. Zbl 1130.76361Barrett, John W.; Garcke, Harald; Nürnberg, Robert 16 2003 Numerical approximation of anisotropic geometric evolution equations in the plane. Zbl 1145.65069Barrett, John W.; Garcke, Harald; Nürnberg, Robert 16 2008 On the stable numerical approximation of two-phase flow with insoluble surfactant. Zbl 1315.35156Barrett, John W.; Garcke, Harald; Nürnberg, Robert 16 2015 Numerical approximation of gradient flows for closed curves in \(\mathbb R^{d}\). Zbl 1185.65027Barrett, John W.; Garcke, Harald; Nürnberg, Robert 15 2010 A stable parametric finite element discretization of two-phase Navier-Stokes flow. Zbl 1320.76059Barrett, John W.; Garcke, Harald; Nürnberg, Robert 15 2015 Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies. Zbl 1205.65263Barrett, John W.; Garcke, Harald; Nürnberg, Robert 14 2010 A diffuse interface model for alloys with multiple components and phases. Zbl 1126.82025Garcke, Harald; Nestler, Britta; Stinner, Bjorn 14 2004 A variational formulation of anisotropic geometric evolution equations in higher dimensions. Zbl 1149.65082Barrett, John W.; Garcke, Harald; Nürnberg, Robert 14 2008 Multi-material phase field approach to structural topology optimization. Zbl 1327.49068Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Rupprecht, Christoph; Styles, Vanessa 14 2014 On a Cahn-Hilliard-Brinkman model for tumor growth and its singular limits. Zbl 1420.35116Ebenbeck, Matthias; Garcke, Harald 14 2019 Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225Elliott, Charles M.; Garcke, Harald 13 1997 Stable finite element approximations of two-phase flow with soluble surfactant. Zbl 1349.76175Barrett, John W.; Garcke, Harald; Nürnberg, Robert 13 2015 Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087Elliott, Charles M.; Garcke, Harald 13 1997 Elastic flow with junctions: variational approximation and applications to nonlinear splines. Zbl 1252.76038Barrett, John W.; Garcke, Harald; Nürnberg, Robert 13 2012 Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: a gradient flow approach. Zbl 1429.35114Garcke, Harald; Knopf, Patrik 13 2020 Allen-Cahn systems with volume constraints. Zbl 1147.49036Garcke, Harald; Nestler, Britta; Stinner, Björn; Wendler, Frank 13 2008 On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth. Zbl 1201.80075Barrett, John W.; Garcke, Harald; Nürnberg, Robert 12 2010 Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid. Zbl 1078.74050Barrett, John W.; Garcke, Harald; Nürnberg, Robert 12 2006 Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method. Zbl 1233.35132Blank, Luise; Butz, Martin; Garcke, Harald 12 2011 Parametric finite element approximations of curvature-driven interface evolutions. Zbl 1455.35185Barrett, John W.; Garcke, Harald; Nürnberg, Robert 12 2020 A coupled surface-Cahn-Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes. Zbl 1338.35222Garcke, Harald; Kampmann, Johannes; Rätz, Andreas; Röger, Matthias 11 2016 Mean curvature flow with triple junctions in higher space dimensions. Zbl 1291.53078Depner, Daniel; Garcke, Harald; Kohsaka, Yoshihito 11 2014 Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow. Zbl 1286.76040Barrett, John W.; Garcke, Harald; Nürnberg, Robert 11 2013 A phase field model for the electromigration of intergranular voids. Zbl 1132.35082Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2007 Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering. Zbl 1410.80015Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2010 Willmore flow of planar networks. Zbl 1436.35233Garcke, Harald; Menzel, Julia; Pluda, Alessandra 10 2019 Anisotropy in multi-phase systems: A phase field approach. Zbl 0959.35169Garcke, Harald; Stoth, Barbara; Nestler, Britta 9 1999 Numerical approximation of the Cahn-Larché equation. Zbl 1099.74063Garcke, Harald; Weikard, Ulrich 9 2005 Curvature driven interface evolution. Zbl 1279.53064Garcke, Harald 9 2013 On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects. Zbl 1456.35091Garcke, Harald; Lam, Kei Fong; Signori, Andrea 9 2021 Solutions of a fourth order degenerate parabolic equation with weak initial trace. Zbl 0945.35049Dal Passo, Roberta; Garcke, Harald 8 1999 Stable numerical approximation of two-phase flow with a Boussinesq-Scriven surface fluid. Zbl 1329.35241Barrett, John W.; Garcke, Harald; Nürnberg, Robert 8 2015 A phase field approach to shape optimization in Navier-Stokes flow with integral state constraints. Zbl 1406.35274Garcke, Harald; Hinze, Michael; Kahle, Christian; Lam, Kei Fong 7 2018 Finite element approximation of one-sided Stefan problems with anisotropic, approximately crystalline, Gibbs-Thomson law. Zbl 1271.80005Barrett, John W.; Garcke, Harald; Nürnberg, Robert 7 2013 Linearized stability analysis of surface diffusion for hypersurfaces with triple lines. Zbl 1263.35031Depner, Daniel; Garcke, Harald 7 2013 Finite element methods for fourth order axisymmetric geometric evolution equations. Zbl 1416.65334Barrett, John W.; Garcke, Harald; Nürnberg, Robert 7 2019 Sharp interface limit for a phase field model in structural optimization. Zbl 1348.35259Blank, Luise; Garcke, Harald; Hecht, Claudia; Rupprecht, Christoph 6 2016 A phase field approach for shape and topology optimization in Stokes flow. Zbl 1329.76108Garcke, Harald; Hecht, Claudia 6 2015 Segmentation and restoration of images on surfaces by parametric active contours with topology changes. Zbl 1405.94014Benninghoff, Heike; Garcke, Harald 6 2016 Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow. Zbl 1342.35218Garcke, Harald; Hecht, Claudia 6 2016 Allen-Cahn and Cahn-Hilliard variational inequalities solved with optimization techniques. Zbl 1356.49009Blank, Luise; Butz, Martin; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa 6 2012 Finite element approximation for the dynamics of asymmetric fluidic biomembranes. Zbl 1394.76064Barrett, John W.; Garcke, Harald; Nürnberg, Robert 6 2017 A mathematical model for grain growth in thin metallic films. Zbl 1205.74138Garcke, Harald; Nestler, Britta 6 2000 Linearized stability analysis of stationary solutions for surface diffusion with boundary conditions. Zbl 1097.35030Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito 6 2005 Travelling wave solutions as dynamic phase transitions in shape memory alloys. Zbl 0829.73007Garcke, Harald 6 1995 Long time existence of solutions to an elastic flow of networks. Zbl 1460.35036Garcke, Harald; Menzel, Julia; Pluda, Alessandra 6 2020 Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature. Zbl 1433.65206Barrett, John W.; Garcke, Harald; Nürnberg, Robert 5 2017 Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation. Zbl 1204.35026Alfaro, Matthieu; Garcke, Harald; Hilhorst, Danielle; Matano, Hiroshi; Schätzle, Reiner 5 2010 Two-phase flow with surfactants: diffuse interface models and their analysis. Zbl 1391.76766Abels, Helmut; Garcke, Harald; Lam, Kei Fong; Weber, Josef 5 2017 Bi-directional diffusion induced grain boundary motion with triple junctions. Zbl 1081.35116Garcke, H.; Styles, Vanessa 5 2004 Stress- and diffusion-induced interface motion: modelling and numerical simulations. Zbl 1128.74004Garcke, Harald; Nürnberg, Robert; Styles, Vanessa 5 2007 Nonlocal Allen-Cahn systems. Analysis and a primal-dual active set method. Zbl 1279.65087Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa 5 2013 Nonlinear stability of stationary solutions for curvature flow with triple junction. Zbl 1187.35013Garcke, Harald; Kohsaka, Yoshihito; Ševčovič, Daniel 5 2009 Variational discretization of axisymmetric curvature flows. Zbl 1419.65051Barrett, John W.; Garcke, Harald; Nürnberg, Robert 5 2019 Efficient image segmentation and restoration using parametric curve evolution with junctions and topology changes. Zbl 1308.94013Benninghoff, Heike; Garcke, Harald 5 2014 Surface diffusion with triple junctions: A stability criterion for stationary solutions. Zbl 1228.35042Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito 4 2010 Finite element approximation for the dynamics of fluidic two-phase biomembranes. Zbl 1383.35153Barrett, John W.; Garcke, Harald; Nürnberg, Robert 4 2017 Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects. Zbl 1428.53104Barrett, John W.; Garcke, Harald; Nürnberg, Robert 4 2016 Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach. Zbl 1352.49046Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian; Lam, Kei Fong 4 2016 Long-time dynamics of the Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions. Zbl 1479.35094Garcke, Harald; Knopf, Patrik; Yayla, Sema 2 2022 Shape and topology optimization involving the eigenvalues of an elastic structure: a multi-phase-field approach. Zbl 1475.35217Garcke, Harald; Hüttl, Paul; Knopf, Patrik 1 2022 On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects. Zbl 1456.35091Garcke, Harald; Lam, Kei Fong; Signori, Andrea 9 2021 Sparse optimal control of a phase field tumor model with mechanical effects. Zbl 1461.49060Garcke, Harald; Lam, Kei Fong; Signori, Andrea 3 2021 Stable approximations for axisymmetric Willmore flow for closed and open surfaces. Zbl 07405585Barrett, John W.; Garcke, Harald; Nürnberg, Robert 2 2021 Cahn-Hilliard-Brinkman systems for tumour growth. Zbl 1480.35411Ebenbeck, Matthias; Garcke, Harald; Nürnberg, Robert 1 2021 On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces. Zbl 1475.35194Garcke, Harald; Matioc, Bogdan-Vasile 1 2021 Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: a gradient flow approach. Zbl 1429.35114Garcke, Harald; Knopf, Patrik 13 2020 Parametric finite element approximations of curvature-driven interface evolutions. Zbl 1455.35185Barrett, John W.; Garcke, Harald; Nürnberg, Robert 12 2020 Long time existence of solutions to an elastic flow of networks. Zbl 1460.35036Garcke, Harald; Menzel, Julia; Pluda, Alessandra 6 2020 Numerical approximation of curve evolutions in Riemannian manifolds. Zbl 1466.65121Barrett, John W.; Garcke, Harald; Nürnberg, Robert 2 2020 On the surface diffusion flow with triple junctions in higher space dimensions. Zbl 1439.53079Garcke, H.; Gößwein, M. 2 2020 Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data. Zbl 1458.92048Agosti, A.; Ciarletta, P.; Garcke, H.; Hinze, M. 2 2020 Long-time dynamics for a Cahn-Hilliard tumor growth model with chemotaxis. Zbl 1446.35221Garcke, Harald; Yayla, Sema 1 2020 Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis. Zbl 1410.35058Ebenbeck, Matthias; Garcke, Harald 24 2019 On a Cahn-Hilliard-Brinkman model for tumor growth and its singular limits. Zbl 1420.35116Ebenbeck, Matthias; Garcke, Harald 14 2019 Willmore flow of planar networks. Zbl 1436.35233Garcke, Harald; Menzel, Julia; Pluda, Alessandra 10 2019 Finite element methods for fourth order axisymmetric geometric evolution equations. Zbl 1416.65334Barrett, John W.; Garcke, Harald; Nürnberg, Robert 7 2019 Variational discretization of axisymmetric curvature flows. Zbl 1419.65051Barrett, John W.; Garcke, Harald; Nürnberg, Robert 5 2019 Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants. Zbl 1404.35340Abels, Helmut; Garcke, Harald; Weber, Josef 3 2019 Optimal control of time-discrete two-phase flow driven by a diffuse-interface model. Zbl 1437.35575Garcke, Harald; Hinze, Michael; Kahle, Christian 3 2019 Stable discretizations of elastic flow in Riemannian manifolds. Zbl 1422.65249Barrett, John W.; Garcke, Harald; Nürnberg, Robert 2 2019 A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis. Zbl 1380.92029Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel 44 2018 Optimal control of treatment time in a diffuse interface model of tumor growth. Zbl 1403.35139Garcke, Harald; Lam, Kei Fong; Rocca, Elisabetta 29 2018 A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities. Zbl 1394.35353Dedè, Luca; Garcke, Harald; Lam, Kei Fong 16 2018 On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms. Zbl 1406.92296Garcke, Harald; Lam, Kei Fong 16 2018 A phase field approach to shape optimization in Navier-Stokes flow with integral state constraints. Zbl 1406.35274Garcke, Harald; Hinze, Michael; Kahle, Christian; Lam, Kei Fong 7 2018 Cahn-Hilliard inpainting with the double obstacle potential. Zbl 1455.94019Garcke, Harald; Lam, Kei Fong; Styles, Vanessa 3 2018 Gradient flow dynamics of two-phase biomembranes: sharp interface variational formulation and finite element approximation. Zbl 1416.74070Barrett, John W.; Garcke, Harald; Nürnberg, Robert 2 2018 Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. Zbl 1375.92011Garcke, Harald; Lam, Kei Fong 41 2017 Analysis of a Cahn-Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis. Zbl 1360.35042Garcke, Harald; Lam, Kei Fong 29 2017 Finite element approximation for the dynamics of asymmetric fluidic biomembranes. Zbl 1394.76064Barrett, John W.; Garcke, Harald; Nürnberg, Robert 6 2017 Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature. Zbl 1433.65206Barrett, John W.; Garcke, Harald; Nürnberg, Robert 5 2017 Two-phase flow with surfactants: diffuse interface models and their analysis. Zbl 1391.76766Abels, Helmut; Garcke, Harald; Lam, Kei Fong; Weber, Josef 5 2017 Finite element approximation for the dynamics of fluidic two-phase biomembranes. Zbl 1383.35153Barrett, John W.; Garcke, Harald; Nürnberg, Robert 4 2017 Mathematical modeling. Zbl 1386.00063Eck, Christof; Garcke, Harald; Knabner, Peter 2 2017 Diffuse interface models for incompressible two-phase flows with different densities. Zbl 1391.76765Abels, Helmut; Garcke, Harald; Grün, Günther; Metzger, Stefan 1 2017 Segmentation of three-dimensional images with parametric active surfaces and topology changes. Zbl 1376.65017Benninghoff, Heike; Garcke, Harald 1 2017 Mathematical modelling. 3rd edition. (Mathematische Modellierung.) Zbl 1368.00002Eck, Christof; Garcke, Harald; Knabner, Peter 1 2017 A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. Zbl 1336.92038Garcke, Harald; Lam, Kei Fong; Sitka, Emanuel; Styles, Vanessa 63 2016 A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow. Zbl 1329.76168Garcke, Harald; Hinze, Michael; Kahle, Christian 27 2016 Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth. Zbl 1434.35255Garcke, Harald; Lam, Kei Fong 24 2016 A stable numerical method for the dynamics of fluidic membranes. Zbl 1391.76298Barrett, John W.; Garcke, Harald; Nürnberg, Robert 20 2016 A coupled surface-Cahn-Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes. Zbl 1338.35222Garcke, Harald; Kampmann, Johannes; Rätz, Andreas; Röger, Matthias 11 2016 Sharp interface limit for a phase field model in structural optimization. Zbl 1348.35259Blank, Luise; Garcke, Harald; Hecht, Claudia; Rupprecht, Christoph 6 2016 Segmentation and restoration of images on surfaces by parametric active contours with topology changes. Zbl 1405.94014Benninghoff, Heike; Garcke, Harald 6 2016 Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow. Zbl 1342.35218Garcke, Harald; Hecht, Claudia 6 2016 Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects. Zbl 1428.53104Barrett, John W.; Garcke, Harald; Nürnberg, Robert 4 2016 Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach. Zbl 1352.49046Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian; Lam, Kei Fong 4 2016 Shape and topology optimization in Stokes flow with a phase field approach. Zbl 1334.49133Garcke, Harald; Hecht, Claudia 4 2016 Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension. Zbl 1335.53079Abels, Helmut; Garcke, Harald; Müller, Lars 4 2016 Image segmentation using parametric contours with free endpoints. Zbl 1408.94048Benninghoff, Heike; Garcke, Harald 1 2016 Numerical approximation of phase field based shape and topology optimization for fluids. Zbl 1322.35113Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian 17 2015 On the stable numerical approximation of two-phase flow with insoluble surfactant. Zbl 1315.35156Barrett, John W.; Garcke, Harald; Nürnberg, Robert 16 2015 A stable parametric finite element discretization of two-phase Navier-Stokes flow. Zbl 1320.76059Barrett, John W.; Garcke, Harald; Nürnberg, Robert 15 2015 Stable finite element approximations of two-phase flow with soluble surfactant. Zbl 1349.76175Barrett, John W.; Garcke, Harald; Nürnberg, Robert 13 2015 Stable numerical approximation of two-phase flow with a Boussinesq-Scriven surface fluid. Zbl 1329.35241Barrett, John W.; Garcke, Harald; Nürnberg, Robert 8 2015 A phase field approach for shape and topology optimization in Stokes flow. Zbl 1329.76108Garcke, Harald; Hecht, Claudia 6 2015 Stability of spherical caps under the volume-preserving mean curvature flow with line tension. Zbl 1314.53115Abels, Helmut; Garcke, Harald; Müller, Lars 3 2015 On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions. Zbl 1366.35006Abels, Helmut; Arab, Nasrin; Garcke, Harald 1 2015 Diffuse interface modelling of soluble surfactants in two-phase flow. Zbl 1319.35309Garcke, Harald; Lam, Kei Fong; Stinner, Björn 30 2014 Relating phase field and sharp interface approaches to structural topology optimization. Zbl 1301.49113Blank, Luise; Garcke, Harald; Farshbaf-Shaker, M. Hassan; Styles, Vanessa 17 2014 Multi-material phase field approach to structural topology optimization. Zbl 1327.49068Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Rupprecht, Christoph; Styles, Vanessa 14 2014 Mean curvature flow with triple junctions in higher space dimensions. Zbl 1291.53078Depner, Daniel; Garcke, Harald; Kohsaka, Yoshihito 11 2014 Efficient image segmentation and restoration using parametric curve evolution with junctions and topology changes. Zbl 1308.94013Benninghoff, Heike; Garcke, Harald 5 2014 Stable phase field approximations of anisotropic solidification. Zbl 1310.65120Barrett, John W.; Garcke, Harald; Nürnberg, Robert 3 2014 Phase field models versus parametric front tracking methods: are they accurate and computationally efficient? Zbl 1388.65096Barrett, John W.; Garcke, Harald; Nürnberg, Robert 2 2014 Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities. Zbl 1273.76421Abels, Helmut; Depner, Daniel; Garcke, Harald 36 2013 On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. Zbl 1347.76052Abels, Helmut; Depner, Daniel; Garcke, Harald 33 2013 Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints. Zbl 1272.65060Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa 17 2013 Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow. Zbl 1286.76040Barrett, John W.; Garcke, Harald; Nürnberg, Robert 11 2013 Curvature driven interface evolution. Zbl 1279.53064Garcke, Harald 9 2013 Finite element approximation of one-sided Stefan problems with anisotropic, approximately crystalline, Gibbs-Thomson law. Zbl 1271.80005Barrett, John W.; Garcke, Harald; Nürnberg, Robert 7 2013 Linearized stability analysis of surface diffusion for hypersurfaces with triple lines. Zbl 1263.35031Depner, Daniel; Garcke, Harald 7 2013 Nonlocal Allen-Cahn systems. Analysis and a primal-dual active set method. Zbl 1279.65087Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa 5 2013 On the stable discretization of strongly anisotropic phase field models with applications to crystal growth. Zbl 1427.74161Barrett, John. W.; Garcke, Harald; Nürnberg, Robert 1 2013 Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Zbl 1242.76342Abels, Helmut; Garcke, Harald; Grün, Günther 146 2012 Phase-field approaches to structural topology optimization. Zbl 1356.49044Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Srisupattarawanit, Tarin; Styles, Vanessa; Voigt, Axel 24 2012 Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. Zbl 1242.65188Barrett, John W.; Garcke, Harald; Nürnberg, Robert 18 2012 Elastic flow with junctions: variational approximation and applications to nonlinear splines. Zbl 1252.76038Barrett, John W.; Garcke, Harald; Nürnberg, Robert 13 2012 Allen-Cahn and Cahn-Hilliard variational inequalities solved with optimization techniques. Zbl 1356.49009Blank, Luise; Butz, Martin; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa 6 2012 The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute. Zbl 1218.65105Barrett, John W.; Garcke, Harald; Nürnberg, Robert 24 2011 Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method. Zbl 1233.35132Blank, Luise; Butz, Martin; Garcke, Harald 12 2011 Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biomembranes. Zbl 1210.35258Farshbaf-Shaker, M. Hassan; Garcke, Harald 4 2011 Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law. Zbl 1235.35286Garcke, Harald; Schaubeck, Stefan 3 2011 Mathematical modelling. 2nd revised ed. (Mathematische Modellierung.) Zbl 1226.00031Eck, Christof; Garcke, Harald; Knabner, Peter 1 2011 Numerical approximation of gradient flows for closed curves in \(\mathbb R^{d}\). Zbl 1185.65027Barrett, John W.; Garcke, Harald; Nürnberg, Robert 15 2010 Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies. Zbl 1205.65263Barrett, John W.; Garcke, Harald; Nürnberg, Robert 14 2010 On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth. Zbl 1201.80075Barrett, John W.; Garcke, Harald; Nürnberg, Robert 12 2010 Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering. Zbl 1410.80015Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2010 Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation. Zbl 1204.35026Alfaro, Matthieu; Garcke, Harald; Hilhorst, Danielle; Matano, Hiroshi; Schätzle, Reiner 5 2010 Surface diffusion with triple junctions: A stability criterion for stationary solutions. Zbl 1228.35042Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito 4 2010 An anisotropic, inhomogeneous, elastically modified Gibbs-Thomson law as singular limit of a diffuse interface model. Zbl 1233.35010Garcke, Harald; Kraus, Christiane 1 2010 Nonlinear stability of stationary solutions for curvature flow with triple junction. Zbl 1187.35013Garcke, Harald; Kohsaka, Yoshihito; Ševčovič, Daniel 5 2009 On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\). Zbl 1145.65068Barrett, John W.; Garcke, Harald; Nürnberg, Robert 44 2008 Parametric approximation of willmore flow and related geometric evolution equations. Zbl 1186.65133Barrett, John W.; Garcke, Harald; Nürnberg, Robert 40 2008 Numerical approximation of anisotropic geometric evolution equations in the plane. Zbl 1145.65069Barrett, John W.; Garcke, Harald; Nürnberg, Robert 16 2008 A variational formulation of anisotropic geometric evolution equations in higher dimensions. Zbl 1149.65082Barrett, John W.; Garcke, Harald; Nürnberg, Robert 14 2008 Allen-Cahn systems with volume constraints. Zbl 1147.49036Garcke, Harald; Nestler, Britta; Stinner, Björn; Wendler, Frank 13 2008 On sharp interface limits of Allen-Cahn/Cahn-Hilliard variational inequalities. Zbl 1165.35406Barrett, John W.; Garcke, Harald; Nürnberg, Robert 4 2008 ...and 42 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,357 Authors 78 Garcke, Harald 41 Nürnberg, Robert 26 Abels, Helmut 26 Barrett, John W. 24 Kim, Junseok 23 Lam, Kei Fong 18 Rocca, Elisabetta 17 Miranville, Alain M. 17 Yang, Xiaofeng 15 Grün, Günther 14 Colli, Pierluigi 14 Signori, Andrea 13 Elliott, Charles M. 13 Kahle, Christian 13 Lowengrub, John Samuel 13 Wise, Steven M. 12 Nestler, Britta 12 Scarpa, Luca 11 Hinze, Michael 11 Styles, Vanessa 11 Sun, Shuyu 11 Wang, Cheng 10 Hintermüller, Michael 10 Olshanskii, Maxim A. 10 Stinner, Bjorn 10 Zhao, Quan 9 Grasselli, Maurizio 9 Kraus, Christiane 9 Li, Buyang 9 Roubíček, Tomáš 9 Sprekels, Jürgen 9 Winkler, Michael 8 Giorgini, Andrea 8 Knopf, Patrik 8 Kou, Jisheng 8 Liu, Chein-Shan 8 Liu, Chun 8 Voigt, Axel 8 Wang, Xiaoming 8 Zhao, Xiaopeng 8 Zhu, Peicheng 7 Blank, Luise 7 Dai, Shibin 7 Deckelnick, Klaus 7 Du, Qiang 7 Frigeri, Sergio 7 Han, Daozhi 7 Jüngel, Ansgar 7 Lee, Hyun Geun 7 Metzger, Stefan 7 Oden, John Tinsley 7 Pozzi, Paola 7 Stoll, Martin 7 Wheeler, Glen E. 7 Wohlmuth, Barbara I. 7 Yang, Junxiang 6 Aland, Sebastian 6 Bao, Weizhu 6 Beneš, Michal 6 Bretin, Elie 6 Chen, Wenbin 6 Dede’, Luca 6 Dong, Suchuan 6 Escher, Joachim 6 Fischer, Julian 6 Fritz, Marvin 6 Giacomelli, Lorenzo 6 Hughes, Thomas J. R. 6 Kovács, Balázs 6 Li, Yibao 6 Liang, Bo 6 Lin, Ping 6 Matthes, Daniel 6 Nochetto, Ricardo Horacio 6 Pluda, Alessandra 6 Shen, Jie 6 Taranets, Roman M. 6 Tomassetti, Giuseppe 6 Xu, Yan 6 Yang, Zhiguo 5 Alber, Hans-Dieter 5 Bartels, Sören 5 Bonetti, Elena 5 Bosch, Jessica 5 Chen, Chuanjun 5 Ebenbeck, Matthias 5 Fabrizio, Mauro 5 Fukao, Takeshi 5 Glasner, Karl B. 5 Gnann, Manuel V. 5 Hecht, Claudia 5 King, John Robert 5 Münch, Andreas 5 Rabczuk, Timon 5 Reusken, Arnold 5 Schneider, Daniel 5 Tavakoli, Rouhollah 5 Van Brummelen, Harald 5 Walker, Shawn W. 5 Wang, Qi ...and 1,257 more Authors all top 5 Cited in 193 Serials 123 Journal of Computational Physics 46 Computer Methods in Applied Mechanics and Engineering 30 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 29 Journal of Scientific Computing 25 Numerische Mathematik 24 Archive for Rational Mechanics and Analysis 24 Journal of Differential Equations 23 Journal of Computational and Applied Mathematics 21 Journal of Mathematical Analysis and Applications 21 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 20 Physica D 20 European Journal of Applied Mathematics 19 SIAM Journal on Numerical Analysis 19 SIAM Journal on Scientific Computing 18 SIAM Journal on Mathematical Analysis 17 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 15 Computers & Mathematics with Applications 15 Applied Mathematics and Optimization 15 Discrete and Continuous Dynamical Systems 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 Nonlinear Analysis. Real World Applications 12 Mathematical Methods in the Applied Sciences 11 Journal of Fluid Mechanics 11 Mathematics of Computation 11 Applied Mathematics and Computation 11 Applied Numerical Mathematics 11 Communications in Computational Physics 10 SIAM Journal on Control and Optimization 10 Communications in Partial Differential Equations 10 SIAM Journal on Applied Mathematics 10 Interfaces and Free Boundaries 9 Calculus of Variations and Partial Differential Equations 9 Advances in Computational Mathematics 9 Discrete and Continuous Dynamical Systems. Series B 8 Applicable Analysis 8 Nonlinearity 8 Computational Mechanics 8 Applied Mathematics Letters 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Computers and Fluids 7 Journal of Mathematical Physics 7 Continuum Mechanics and Thermodynamics 7 NoDEA. Nonlinear Differential Equations and Applications 7 Journal of Evolution Equations 7 Discrete and Continuous Dynamical Systems. Series S 6 Numerical Methods for Partial Differential Equations 6 Applied Mathematical Modelling 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Communications on Pure and Applied Analysis 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Journal of Nonlinear Science 5 Journal of Mathematical Fluid Mechanics 5 Communications in Nonlinear Science and Numerical Simulation 4 Physica A 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 International Journal for Numerical Methods in Engineering 4 Mathematische Annalen 4 Mathematische Nachrichten 4 Proceedings of the American Mathematical Society 4 Transactions of the American Mathematical Society 4 European Journal of Mechanics. B. Fluids 4 Analysis (München) 4 Optimization and Engineering 4 Archives of Computational Methods in Engineering 4 Computational Methods in Applied Mathematics 4 Milan Journal of Mathematics 4 Multiscale Modeling & Simulation 4 Advances in Nonlinear Analysis 4 Geometric Flows 4 AIMS Mathematics 3 Journal of Mathematical Biology 3 Mathematics and Computers in Simulation 3 Quarterly of Applied Mathematics 3 Asymptotic Analysis 3 Computational Geosciences 3 SIAM Journal on Applied Dynamical Systems 3 Boundary Value Problems 3 SIAM Journal on Imaging Sciences 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Computer Physics Communications 2 Communications on Pure and Applied Mathematics 2 International Journal of Engineering Science 2 Inverse Problems 2 Journal of Engineering Mathematics 2 Journal of the Mechanics and Physics of Solids 2 Journal of Statistical Physics 2 Bulletin of Mathematical Biology 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 BIT 2 Calcolo 2 Journal of Optimization Theory and Applications 2 Journal für die Reine und Angewandte Mathematik 2 Zeitschrift für Analysis und ihre Anwendungen 2 Acta Applicandae Mathematicae 2 Mathematical and Computer Modelling 2 Japan Journal of Industrial and Applied Mathematics 2 The Journal of Geometric Analysis 2 Applications of Mathematics 2 Numerical Algorithms ...and 93 more Serials all top 5 Cited in 37 Fields 705 Partial differential equations (35-XX) 447 Numerical analysis (65-XX) 412 Fluid mechanics (76-XX) 196 Mechanics of deformable solids (74-XX) 127 Biology and other natural sciences (92-XX) 126 Calculus of variations and optimal control; optimization (49-XX) 93 Statistical mechanics, structure of matter (82-XX) 84 Differential geometry (53-XX) 63 Classical thermodynamics, heat transfer (80-XX) 32 Dynamical systems and ergodic theory (37-XX) 20 Global analysis, analysis on manifolds (58-XX) 18 Operations research, mathematical programming (90-XX) 14 Optics, electromagnetic theory (78-XX) 13 Integral equations (45-XX) 11 Probability theory and stochastic processes (60-XX) 10 Operator theory (47-XX) 10 Computer science (68-XX) 9 Systems theory; control (93-XX) 8 Ordinary differential equations (34-XX) 7 Functional analysis (46-XX) 7 Geophysics (86-XX) 6 Information and communication theory, circuits (94-XX) 5 Approximations and expansions (41-XX) 4 Quantum theory (81-XX) 3 Combinatorics (05-XX) 3 Real functions (26-XX) 3 Functions of a complex variable (30-XX) 3 Statistics (62-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Potential theory (31-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of particles and systems (70-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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