Edit Profile Garcke, Harald Compute Distance To: Compute Author ID: garcke.harald Published as: Garcke, H.; Garcke, Harald External Links: MGP · Wikidata · GND Documents Indexed: 145 Publications since 1993, including 5 Books all top 5 Co-Authors 9 single-authored 40 Barrett, John W. 39 Nürnberg, Robert 15 Lam, Kei Fong 10 Styles, Vanessa 9 Abels, Helmut 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 Grün, Günther 4 Knabner, Peter 4 Sarbu, Lavinia 4 Stoth, Barbara E. E. 4 Weikard, Ulrich 3 Blowey, James F. 3 Dal Passo, Roberta 2 Butz, Martin V. 2 Ebenbeck, Matthias 2 Farshbaf-Shaker, Mohammad Hassan 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 1 Agosti, Abramo 1 Alfaro, Matthieu 1 Arab, Nasrin 1 Bertsch, Michiel 1 Bronsard, Lia 1 Ciarletta, Pasquale 1 Dede, Luca 1 Escher, Joachim 1 Gößwein, M. 1 Hassan Farshbaf-Shaker, M. 1 Hilhorst, Danielle 1 Kampmann, Johannes 1 Knopf, Patrik 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 Yayla, Sema all top 5 Serials 7 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 SIAM Journal on Mathematical Analysis 7 Interfaces and Free Boundaries 6 IMA Journal of Numerical Analysis 6 Numerische Mathematik 5 Journal of Computational Physics 5 Advances in Mathematical Sciences and Applications 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 Journal of Differential Equations 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 Springer-Lehrbuch 2 Mathematics of Computation 2 Applied Mathematics and Optimization 2 Hokkaido Mathematical Journal 2 Mathematische Nachrichten 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 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 SIAM Journal on Imaging Sciences 2 Discrete and Continuous Dynamical Systems. Series S 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 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Applied Numerical Mathematics 1 Communications in Partial Differential Equations 1 Journal of Mathematical Imaging and Vision 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 Geometric Flows 1 AIMS Mathematics 1 Springer Undergraduate Mathematics Series 1 SMAI Journal of Computational Mathematics all top 5 Fields 111 Partial differential equations (35-XX) 56 Numerical analysis (65-XX) 42 Fluid mechanics (76-XX) 34 Mechanics of deformable solids (74-XX) 31 Calculus of variations and optimal control; optimization (49-XX) 26 Differential geometry (53-XX) 22 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 Information and communication theory, circuits (94-XX) 4 Ordinary differential equations (34-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Operations research, mathematical programming (90-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Computer science (68-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 128 Publications have been cited 1,765 times in 884 Documents Cited by ▼ Year ▼ On the Cahn-Hilliard equation with degenerate mobility. Zbl 0856.35071Elliott, Charles M.; Garcke, Harald 166 1996 Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Zbl 1242.76342Abels, Helmut; Garcke, Harald; Grün, Günther 116 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 82 1998 Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. Zbl 0947.65109Barrett, John W.; Blowey, James F.; Garcke, Harald 77 1999 A parametric finite element method for fourth order geometric evolution equations. Zbl 1112.65093Barrett, John W.; Garcke, Harald; Nürnberg, Robert 45 2007 On anisotropic order parameter models for multi-phase systems and their sharp interface limits. Zbl 0936.82010Garcke, Harald; Nestler, Britta; Stoth, Barbara 43 1998 A multiphase field concept: Numerical simulations of moving phase boundaries and multiple junctions. Zbl 0942.35095Garcke, Harald; Nestler, Britta; Stoth, Barbara 40 1999 On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\). Zbl 1145.65068Barrett, John W.; Garcke, Harald; Nürnberg, Robert 37 2008 A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. Zbl 1336.92038Garcke, Harald; Lam, Kei Fong; Sitka, Emanuel; Styles, Vanessa 36 2016 Parametric approximation of willmore flow and related geometric evolution equations. Zbl 1186.65133Barrett, John W.; Garcke, Harald; Nürnberg, Robert 36 2008 The thin viscous flow equation in higher space dimensions. Zbl 0954.35035Bertsch, Michiel; Dal Passo, Roberta; Garcke, Harald; Grün, Günther 35 1998 On Cahn-Hilliard systems with elasticity. Zbl 1130.74037Garcke, Harald 31 2003 On fully practical finite element approximations of degenerate Cahn-Hilliard systems. Zbl 0987.35071Barrett, John W.; Blowey, James F.; Garcke, Harald 31 2001 Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Zbl 0913.65084Barrett, John W.; Blowey, James F.; Garcke, Harald 31 1998 On the variational approximation of combined second and fourth order geometric evolution equations. Zbl 1148.65074Barrett, John W.; Garcke, Harald; Nürnberg, Robert 30 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 29 2013 A singular limit for a system of degenerate Cahn-Hilliard equations. Zbl 0988.35019Garcke, Harald; Novick-Cohen, Amy 28 2000 Existence results for diffusive surface motion laws. Zbl 0876.35050Elliott, Charles M.; Garcke, Harald 28 1997 Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. Zbl 1375.92011Garcke, Harald; Lam, Kei Fong 27 2017 Surfactant spreading on thin viscous films: nonnegative solutions of a coupled degenerate system. Zbl 1102.35056Garcke, Harald; Wieland, Sandra 26 2006 A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis. Zbl 1380.92029Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel 24 2018 Diffuse interface modelling of soluble surfactants in two-phase flow. Zbl 1319.35309Garcke, Harald; Lam, Kei Fong; Stinner, Björn 23 2014 On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. Zbl 1347.76052Abels, Helmut; Depner, Daniel; Garcke, Harald 23 2013 On a Cahn–Hilliard model for phase separation with elastic misfit. Zbl 1072.35081Garcke, Harald 21 2005 Analysis of a Cahn-Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis. Zbl 1360.35042Garcke, Harald; Lam, Kei Fong 18 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 17 2016 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 The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute. Zbl 1218.65105Barrett, John W.; Garcke, Harald; Nürnberg, Robert 16 2011 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 Optimal control of treatment time in a diffuse interface model of tumor growth. Zbl 1403.35139Garcke, Harald; Lam, Kei Fong; Rocca, Elisabetta 15 2018 Phase-field approaches to structural topology optimization. Zbl 1356.49044Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Srisupattarawanit, Tarin; Styles, Vanessa; Voigt, Axel 15 2012 A diffuse interface model for alloys with multiple components and phases. Zbl 1126.82025Garcke, Harald; Nestler, Britta; Stinner, Bjorn 15 2004 Finite element approximation of surfactant spreading on a thin film. Zbl 1130.76361Barrett, John W.; Garcke, Harald; Nürnberg, Robert 15 2003 The Cahn-Hilliard equation with elasticity – finite element approximation and qualitative studies. Zbl 0972.35164Garcke, Harald; Rumpf, Martin; Weikard, Ulrich 15 2001 Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087Elliott, Charles M.; Garcke, Harald 15 1997 A stable numerical method for the dynamics of fluidic membranes. Zbl 1391.76298Barrett, John W.; Garcke, Harald; Nürnberg, Robert 14 2016 On the stable numerical approximation of two-phase flow with insoluble surfactant. Zbl 1315.35156Barrett, John W.; Garcke, Harald; Nürnberg, Robert 14 2015 Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis. Zbl 1410.35058Ebenbeck, Matthias; Garcke, Harald 13 2019 Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. Zbl 1242.65188Barrett, John W.; Garcke, Harald; Nürnberg, Robert 13 2012 Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies. Zbl 1205.65263Barrett, John W.; Garcke, Harald; Nürnberg, Robert 13 2010 Allen-Cahn systems with volume constraints. Zbl 1147.49036Garcke, Harald; Nestler, Britta; Stinner, Björn; Wendler, Frank 13 2008 Relating phase field and sharp interface approaches to structural topology optimization. Zbl 1301.49113Blank, Luise; Garcke, Harald; Farshbaf-Shaker, M. Hassan; Styles, Vanessa 12 2014 Numerical approximation of gradient flows for closed curves in \(\mathbb R^{d}\). Zbl 1185.65027Barrett, John W.; Garcke, Harald; Nürnberg, Robert 12 2010 Second order phase field asymptotics for multi-component systems. Zbl 1106.35116Garcke, Harald; Stinner, Björn 12 2006 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 Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225Elliott, Charles M.; Garcke, Harald 12 1997 Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth. Zbl 1434.35255Garcke, Harald; Lam, Kei Fong 11 2016 Stable finite element approximations of two-phase flow with soluble surfactant. Zbl 1349.76175Barrett, John W.; Garcke, Harald; Nürnberg, Robert 11 2015 Multi-material phase field approach to structural topology optimization. Zbl 1327.49068Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Rupprecht, Christoph; Styles, Vanessa 11 2014 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 11 2010 On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms. Zbl 1406.92296Garcke, Harald; Lam, Kei Fong 10 2018 Numerical approximation of phase field based shape and topology optimization for fluids. Zbl 1322.35113Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian 10 2015 A stable parametric finite element discretization of two-phase Navier-Stokes flow. Zbl 1320.76059Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2015 Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow. Zbl 1286.76040Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2013 Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method. Zbl 1233.35132Blank, Luise; Butz, Martin; Garcke, Harald 10 2011 Numerical approximation of anisotropic geometric evolution equations in the plane. Zbl 1145.65069Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2008 A variational formulation of anisotropic geometric evolution equations in higher dimensions. Zbl 1149.65082Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2008 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 9 2010 Anisotropy in multi-phase systems: A phase field approach. Zbl 0959.35169Garcke, Harald; Stoth, Barbara; Nestler, Britta 9 1999 Mean curvature flow with triple junctions in higher space dimensions. Zbl 1291.53078Depner, Daniel; Garcke, Harald; Kohsaka, Yoshihito 8 2014 A phase field model for the electromigration of intergranular voids. Zbl 1132.35082Barrett, John W.; Garcke, Harald; Nürnberg, Robert 8 2007 Numerical approximation of the Cahn-Larché equation. Zbl 1099.74063Garcke, Harald; Weikard, Ulrich 8 2005 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 7 2016 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 Elastic flow with junctions: variational approximation and applications to nonlinear splines. Zbl 1252.76038Barrett, John W.; Garcke, Harald; Nürnberg, Robert 7 2012 Solutions of a fourth order degenerate parabolic equation with weak initial trace. Zbl 0945.35049Dal Passo, Roberta; Garcke, Harald 7 1999 Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: a gradient flow approach. Zbl 1429.35114Garcke, Harald; Knopf, Patrik 6 2020 On a Cahn-Hilliard-Brinkman model for tumor growth and its singular limits. Zbl 1420.35116Ebenbeck, Matthias; Garcke, Harald 6 2019 A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities. Zbl 1394.35353Dedè, Luca; Garcke, Harald; Lam, Kei Fong 6 2018 Finite element approximation for the dynamics of asymmetric fluidic biomembranes. Zbl 1394.76064Barrett, John W.; Garcke, Harald; Nürnberg, Robert 6 2017 Stable numerical approximation of two-phase flow with a Boussinesq-Scriven surface fluid. Zbl 1329.35241Barrett, John W.; Garcke, Harald; Nürnberg, Robert 6 2015 Curvature driven interface evolution. Zbl 1279.53064Garcke, Harald 6 2013 Linearized stability analysis of surface diffusion for hypersurfaces with triple lines. Zbl 1263.35031Depner, Daniel; Garcke, Harald 6 2013 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 Linearized stability analysis of stationary solutions for surface diffusion with boundary conditions. Zbl 1097.35030Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito 6 2005 A phase-field model for the solidification process in multicomponent alloys. Zbl 1061.80004Garcke, H.; Nestler, B.; Stinner, B. 6 2003 A mathematical model for grain growth in thin metallic films. Zbl 1205.74138Garcke, Harald; Nestler, Britta 6 2000 Travelling wave solutions as dynamic phase transitions in shape memory alloys. Zbl 0829.73007Garcke, Harald 6 1995 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 Segmentation and restoration of images on surfaces by parametric active contours with topology changes. Zbl 1405.94014Benninghoff, Heike; Garcke, Harald 5 2016 A phase field approach for shape and topology optimization in Stokes flow. Zbl 1329.76108Garcke, Harald; Hecht, Claudia 5 2015 Efficient image segmentation and restoration using parametric curve evolution with junctions and topology changes. Zbl 1308.94013Benninghoff, Heike; Garcke, Harald 5 2014 Nonlocal Allen-Cahn systems. Analysis and a primal-dual active set method. Zbl 1279.65087Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa 5 2013 Stress- and diffusion-induced interface motion: modelling and numerical simulations. Zbl 1128.74004Garcke, Harald; Nürnberg, Robert; Styles, Vanessa 5 2007 Bi-directional diffusion induced grain boundary motion with triple junctions. Zbl 1081.35116Garcke, H.; Styles, Vanessa 5 2004 Willmore flow of planar networks. Zbl 1436.35233Garcke, Harald; Menzel, Julia; Pluda, Alessandra 4 2019 Sharp interface limit for a phase field model in structural optimization. Zbl 1348.35259Blank, Luise; Garcke, Harald; Hecht, Claudia; Rupprecht, Christoph 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 Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biomembranes. Zbl 1210.35258Farshbaf-Shaker, M. Hassan; Garcke, Harald 4 2011 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 4 2010 Surface diffusion with triple junctions: A stability criterion for stationary solutions. Zbl 1228.35042Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito 4 2010 On sharp interface limits of Allen-Cahn/Cahn-Hilliard variational inequalities. Zbl 1165.35406Barrett, John W.; Garcke, Harald; Nürnberg, Robert 4 2008 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 3 2016 Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects. Zbl 1428.53104Barrett, John W.; Garcke, Harald; Nürnberg, Robert 3 2016 Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow. Zbl 1342.35218Garcke, Harald; Hecht, Claudia 3 2016 Shape and topology optimization in Stokes flow with a phase field approach. Zbl 1334.49133Garcke, Harald; Hecht, Claudia 3 2016 The \(\Gamma\)-limit of the Ginzburg-Landau energy in an elastic medium. Zbl 1193.49054Garcke, Harald 3 2008 Nonlinear stability of stationary solutions for surface diffusion with boundary conditions. Zbl 1167.35005Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito 3 2008 Mathematical modelling. Zbl 1223.00014Eck, Christof; Garcke, Harald; Knabner, Peter 3 2008 On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects. Zbl 1456.35091Garcke, Harald; Lam, Kei Fong; Signori, Andrea 1 2021 Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: a gradient flow approach. Zbl 1429.35114Garcke, Harald; Knopf, Patrik 6 2020 Parametric finite element approximations of curvature-driven interface evolutions. Zbl 1455.35185Barrett, 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. 1 2020 Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis. Zbl 1410.35058Ebenbeck, Matthias; Garcke, Harald 13 2019 On a Cahn-Hilliard-Brinkman model for tumor growth and its singular limits. Zbl 1420.35116Ebenbeck, Matthias; Garcke, Harald 6 2019 Willmore flow of planar networks. Zbl 1436.35233Garcke, Harald; Menzel, Julia; Pluda, Alessandra 4 2019 Optimal control of time-discrete two-phase flow driven by a diffuse-interface model. Zbl 1437.35575Garcke, Harald; Hinze, Michael; Kahle, Christian 2 2019 Variational discretization of axisymmetric curvature flows. Zbl 1419.65051Barrett, John W.; Garcke, Harald; Nürnberg, Robert 1 2019 A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis. Zbl 1380.92029Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel 24 2018 Optimal control of treatment time in a diffuse interface model of tumor growth. Zbl 1403.35139Garcke, Harald; Lam, Kei Fong; Rocca, Elisabetta 15 2018 On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms. Zbl 1406.92296Garcke, Harald; Lam, Kei Fong 10 2018 A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities. Zbl 1394.35353Dedè, Luca; Garcke, Harald; Lam, Kei Fong 6 2018 Cahn-Hilliard inpainting with the double obstacle potential. Zbl 1455.94019Garcke, Harald; Lam, Kei Fong; Styles, Vanessa 1 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 1 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 1 2018 Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. Zbl 1375.92011Garcke, Harald; Lam, Kei Fong 27 2017 Analysis of a Cahn-Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis. Zbl 1360.35042Garcke, Harald; Lam, Kei Fong 18 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 2 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 A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. Zbl 1336.92038Garcke, Harald; Lam, Kei Fong; Sitka, Emanuel; Styles, Vanessa 36 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 17 2016 A stable numerical method for the dynamics of fluidic membranes. Zbl 1391.76298Barrett, John W.; Garcke, Harald; Nürnberg, Robert 14 2016 Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth. Zbl 1434.35255Garcke, Harald; Lam, Kei Fong 11 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 7 2016 Segmentation and restoration of images on surfaces by parametric active contours with topology changes. Zbl 1405.94014Benninghoff, Heike; Garcke, Harald 5 2016 Sharp interface limit for a phase field model in structural optimization. Zbl 1348.35259Blank, Luise; Garcke, Harald; Hecht, Claudia; Rupprecht, Christoph 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 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 3 2016 Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects. Zbl 1428.53104Barrett, John W.; Garcke, Harald; Nürnberg, Robert 3 2016 Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow. Zbl 1342.35218Garcke, Harald; Hecht, Claudia 3 2016 Shape and topology optimization in Stokes flow with a phase field approach. Zbl 1334.49133Garcke, Harald; Hecht, Claudia 3 2016 Image segmentation using parametric contours with free endpoints. Zbl 1408.94048Benninghoff, Heike; Garcke, Harald 1 2016 On the stable numerical approximation of two-phase flow with insoluble surfactant. Zbl 1315.35156Barrett, John W.; Garcke, Harald; Nürnberg, Robert 14 2015 Stable finite element approximations of two-phase flow with soluble surfactant. Zbl 1349.76175Barrett, John W.; Garcke, Harald; Nürnberg, Robert 11 2015 Numerical approximation of phase field based shape and topology optimization for fluids. Zbl 1322.35113Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian 10 2015 A stable parametric finite element discretization of two-phase Navier-Stokes flow. Zbl 1320.76059Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2015 Stable numerical approximation of two-phase flow with a Boussinesq-Scriven surface fluid. Zbl 1329.35241Barrett, John W.; Garcke, Harald; Nürnberg, Robert 6 2015 A phase field approach for shape and topology optimization in Stokes flow. Zbl 1329.76108Garcke, Harald; Hecht, Claudia 5 2015 Stability of spherical caps under the volume-preserving mean curvature flow with line tension. Zbl 1314.53115Abels, Helmut; Garcke, Harald; Müller, Lars 2 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 23 2014 Relating phase field and sharp interface approaches to structural topology optimization. Zbl 1301.49113Blank, Luise; Garcke, Harald; Farshbaf-Shaker, M. Hassan; Styles, Vanessa 12 2014 Multi-material phase field approach to structural topology optimization. Zbl 1327.49068Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Rupprecht, Christoph; Styles, Vanessa 11 2014 Mean curvature flow with triple junctions in higher space dimensions. Zbl 1291.53078Depner, Daniel; Garcke, Harald; Kohsaka, Yoshihito 8 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 2 2014 Phase field models versus parametric front tracking methods: are they accurate and computationally efficient? Zbl 1388.65096Barrett, John W.; Garcke, Harald; Nürnberg, Robert 1 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 29 2013 On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. Zbl 1347.76052Abels, Helmut; Depner, Daniel; Garcke, Harald 23 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 10 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 Curvature driven interface evolution. Zbl 1279.53064Garcke, Harald 6 2013 Linearized stability analysis of surface diffusion for hypersurfaces with triple lines. Zbl 1263.35031Depner, Daniel; Garcke, Harald 6 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 116 2012 Phase-field approaches to structural topology optimization. Zbl 1356.49044Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Srisupattarawanit, Tarin; Styles, Vanessa; Voigt, Axel 15 2012 Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. Zbl 1242.65188Barrett, John W.; Garcke, Harald; Nürnberg, Robert 13 2012 Elastic flow with junctions: variational approximation and applications to nonlinear splines. Zbl 1252.76038Barrett, John W.; Garcke, Harald; Nürnberg, Robert 7 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 16 2011 Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method. Zbl 1233.35132Blank, Luise; Butz, Martin; Garcke, Harald 10 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 1 2011 Mathematical modelling. 2nd revised ed. Zbl 1226.00031Eck, Christof; Garcke, Harald; Knabner, Peter 1 2011 Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies. Zbl 1205.65263Barrett, John W.; Garcke, Harald; Nürnberg, Robert 13 2010 Numerical approximation of gradient flows for closed curves in \(\mathbb R^{d}\). Zbl 1185.65027Barrett, John W.; Garcke, Harald; Nürnberg, Robert 12 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 11 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 9 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 4 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 2 2009 On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\). Zbl 1145.65068Barrett, John W.; Garcke, Harald; Nürnberg, Robert 37 2008 Parametric approximation of willmore flow and related geometric evolution equations. Zbl 1186.65133Barrett, John W.; Garcke, Harald; Nürnberg, Robert 36 2008 Allen-Cahn systems with volume constraints. Zbl 1147.49036Garcke, Harald; Nestler, Britta; Stinner, Björn; Wendler, Frank 13 2008 Numerical approximation of anisotropic geometric evolution equations in the plane. Zbl 1145.65069Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2008 A variational formulation of anisotropic geometric evolution equations in higher dimensions. Zbl 1149.65082Barrett, John W.; Garcke, Harald; Nürnberg, Robert 10 2008 On sharp interface limits of Allen-Cahn/Cahn-Hilliard variational inequalities. Zbl 1165.35406Barrett, John W.; Garcke, Harald; Nürnberg, Robert 4 2008 The \(\Gamma\)-limit of the Ginzburg-Landau energy in an elastic medium. Zbl 1193.49054Garcke, Harald 3 2008 Nonlinear stability of stationary solutions for surface diffusion with boundary conditions. Zbl 1167.35005Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito 3 2008 Mathematical modelling. Zbl 1223.00014Eck, Christof; Garcke, Harald; Knabner, Peter 3 2008 Mini-workshop: Mathematics of biological membranes. Abstracts from the mini-workshop held August 31 – September 6, 2008. Zbl 1177.74021Garcke, Harald (ed.); Niethammer, Barbara (ed.); Peletier, Mark A. (ed.); Röger, Matthias (ed.) 1 2008 A parametric finite element method for fourth order geometric evolution equations. Zbl 1112.65093Barrett, John W.; Garcke, Harald; Nürnberg, Robert 45 2007 On the variational approximation of combined second and fourth order geometric evolution equations. Zbl 1148.65074Barrett, John W.; Garcke, Harald; Nürnberg, Robert 30 2007 A phase field model for the electromigration of intergranular voids. Zbl 1132.35082Barrett, John W.; Garcke, Harald; Nürnberg, Robert 8 2007 Stress- and diffusion-induced interface motion: modelling and numerical simulations. Zbl 1128.74004Garcke, Harald; Nürnberg, Robert; Styles, Vanessa 5 2007 Surfactant spreading on thin viscous films: nonnegative solutions of a coupled degenerate system. Zbl 1102.35056Garcke, Harald; Wieland, Sandra 26 2006 Second order phase field asymptotics for multi-component systems. Zbl 1106.35116Garcke, Harald; Stinner, Björn 12 2006 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 On asymptotic limits of Cahn-Hilliard systems with elastic misfit. Zbl 1366.74055Garcke, Harald; Kwak, David Jung Chul 3 2006 Multiscale problems in solidification processes. Zbl 1366.80004Eck, Christof; Garcke, Harald; Stinner, Björn 1 2006 On a Cahn–Hilliard model for phase separation with elastic misfit. Zbl 1072.35081Garcke, Harald 21 2005 ...and 28 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,167 Authors 71 Garcke, Harald 34 Nürnberg, Robert 25 Barrett, John W. 21 Abels, Helmut 19 Lam, Kei Fong 16 Kim, Junseok 13 Miranville, Alain M. 13 Nestler, Britta 12 Elliott, Charles M. 12 Grün, Günther 12 Lowengrub, John Samuel 12 Rocca, Elisabetta 11 Kahle, Christian 10 Sun, Shuyu 10 Wise, Steven M. 9 Grasselli, Maurizio 9 Kraus, Christiane 9 Roubíček, Tomáš 9 Stinner, Bjorn 9 Styles, Vanessa 8 Colli, Pierluigi 8 Hinze, Michael 8 Wheeler, Glen E. 8 Winkler, Michael 8 Yang, Xiaofeng 8 Zhu, Peicheng 7 Blank, Luise 7 Du, Qiang 7 Giorgini, Andrea 7 Kou, Jisheng 7 Nochetto, Ricardo Horacio 7 Olshanskii, Maxim A. 7 Voigt, Axel 7 Wang, Cheng 6 Dai, Shibin 6 Dede, Luca 6 Dong, Suchuan 6 Escher, Joachim 6 Frigeri, Sergio 6 Giacomelli, Lorenzo 6 Hughes, Thomas J. R. 6 Lee, Hyun Geun 6 Liu, Chein-Shan 6 Matthes, Daniel 6 Metzger, Stefan 6 Pozzi, Paola 6 Scarpa, Luca 6 Signori, Andrea 6 Stoll, Martin 6 Taranets, Roman M. 6 Tomassetti, Giuseppe 6 Wang, Xiaoming 6 Yang, Zhiguo 6 Zhao, Xiaopeng 5 Aland, Sebastian 5 Alber, Hans-Dieter 5 Bonetti, Elena 5 Bretin, Elie 5 Chugunova, Marina A. 5 Deckelnick, Klaus 5 Fabrizio, Mauro 5 Fischer, Julian 5 Glasner, Karl B. 5 Hecht, Claudia 5 Hintermüller, Michael 5 Jüngel, Ansgar 5 King, John Robert 5 Liang, Bo 5 Lin, Ping 5 Selzer, Michael 5 Shen, Jie 5 Tavakoli, Rouhollah 5 Van Brummelen, Harald 5 Wang, Qi 5 Xu, Yan 5 Zhao, Quan 4 Baňas, L’ubomír 4 Bänsch, Eberhard 4 Bartels, Sören 4 Beneš, Michal 4 Bertozzi, Andrea Louise 4 Bosch, Jessica 4 Boyer, Franck 4 Burger, Martin 4 Calo, Victor Manuel 4 Depner, Daniel 4 Ebenbeck, Matthias 4 Esedoglu, Selim 4 Farshbaf-Shaker, Mohammad Hassan 4 Fukao, Takeshi 4 Gal, Ciprian Gheorghe Sorin 4 Giesselmann, Jan 4 Giorgi, Claudio 4 Gnann, Manuel V. 4 Guo, Ruihan 4 Han, Daozhi 4 Heida, Martin 4 Knabner, Peter 4 Knopf, Patrik 4 Knüpfer, Hans ...and 1,067 more Authors all top 5 Cited in 169 Serials 105 Journal of Computational Physics 34 Computer Methods in Applied Mechanics and Engineering 23 Archive for Rational Mechanics and Analysis 23 Journal of Scientific Computing 23 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 22 Numerische Mathematik 21 Journal of Mathematical Analysis and Applications 20 Journal of Computational and Applied Mathematics 20 Journal of Differential Equations 19 Physica D 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 European Journal of Applied Mathematics 15 SIAM Journal on Mathematical Analysis 15 SIAM Journal on Scientific Computing 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 SIAM Journal on Numerical Analysis 13 Computers & Mathematics with Applications 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 Mathematical Methods in the Applied Sciences 12 Discrete and Continuous Dynamical Systems 11 Nonlinear Analysis. Real World Applications 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Applied Mathematics and Optimization 10 SIAM Journal on Control and Optimization 9 Journal of Fluid Mechanics 9 Mathematics of Computation 9 Applied Mathematics and Computation 9 Applied Numerical Mathematics 9 SIAM Journal on Applied Mathematics 8 Computational Mechanics 8 Calculus of Variations and Partial Differential Equations 8 Advances in Computational Mathematics 7 Journal of Mathematical Physics 7 Communications in Partial Differential Equations 7 Continuum Mechanics and Thermodynamics 7 Interfaces and Free Boundaries 6 Applicable Analysis 6 Nonlinearity 6 Numerical Methods for Partial Differential Equations 6 Applied Mathematics Letters 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Discrete and Continuous Dynamical Systems. Series S 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 NoDEA. Nonlinear Differential Equations and Applications 5 Discrete and Continuous Dynamical Systems. Series B 4 Physica A 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 International Journal for Numerical Methods in Engineering 4 Mathematics and Computers in Simulation 4 Mathematische Nachrichten 4 Applied Mathematical Modelling 4 Journal of Nonlinear Science 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Journal of Mathematical Fluid Mechanics 4 Journal of Evolution Equations 4 Archives of Computational Methods in Engineering 4 Communications on Pure and Applied Analysis 4 Geometric Flows 3 Computers and Fluids 3 International Journal of Engineering Science 3 Journal of Mathematical Biology 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 3 Quarterly of Applied Mathematics 3 Transactions of the American Mathematical Society 3 European Journal of Mechanics. B. Fluids 3 Analysis (München) 3 Computational Geosciences 3 Milan Journal of Mathematics 3 Multiscale Modeling & Simulation 3 Boundary Value Problems 3 Advances in Nonlinear Analysis 2 Computer Physics Communications 2 Communications on Pure and Applied Mathematics 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 für die Reine und Angewandte Mathematik 2 Zeitschrift für Analysis und ihre Anwendungen 2 Mathematical and Computer Modelling 2 Asymptotic Analysis 2 Japan Journal of Industrial and Applied Mathematics 2 Applications of Mathematics 2 Numerical Algorithms 2 International Journal of Computer Mathematics 2 Journal of Elasticity 2 Journal of Mathematical Imaging and Vision 2 Journal of Mathematical Sciences (New York) 2 Computing and Visualization in Science 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Acta Mathematica Sinica. English Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Stochastics and Dynamics 2 SIAM Journal on Applied Dynamical Systems 2 Structural and Multidisciplinary Optimization 2 SIAM Journal on Imaging Sciences 2 Journal of Theoretical Biology ...and 69 more Serials all top 5 Cited in 37 Fields 560 Partial differential equations (35-XX) 342 Numerical analysis (65-XX) 327 Fluid mechanics (76-XX) 162 Mechanics of deformable solids (74-XX) 94 Biology and other natural sciences (92-XX) 91 Calculus of variations and optimal control; optimization (49-XX) 79 Statistical mechanics, structure of matter (82-XX) 67 Differential geometry (53-XX) 62 Classical thermodynamics, heat transfer (80-XX) 25 Dynamical systems and ergodic theory (37-XX) 19 Global analysis, analysis on manifolds (58-XX) 12 Integral equations (45-XX) 12 Optics, electromagnetic theory (78-XX) 10 Operations research, mathematical programming (90-XX) 9 Ordinary differential equations (34-XX) 9 Computer science (68-XX) 8 Operator theory (47-XX) 8 Probability theory and stochastic processes (60-XX) 6 Functional analysis (46-XX) 6 Geophysics (86-XX) 6 Systems theory; control (93-XX) 6 Information and communication theory, circuits (94-XX) 4 Approximations and expansions (41-XX) 3 Combinatorics (05-XX) 3 Statistics (62-XX) 2 Real functions (26-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-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) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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