Edit Profile (opens in new tab) Elliott, Charles M. Compute Distance To: Compute Author ID: elliott.charles-m Published as: Elliott, Charles M.; Elliott, C. M.; Elliott, Charlie M.; M. Elliott, Charles; Elliott, Charles; Elliott, C. Homepage: http://www2.warwick.ac.uk/fac/sci/maths/people/staff/charles_elliott/ External Links: MGP · dblp Documents Indexed: 149 Publications since 1978, including 1 Book 10 Contributions as Editor Co-Authors: 93 Co-Authors with 147 Joint Publications 2,517 Co-Co-Authors all top 5 Co-Authors 7 single-authored 18 Deckelnick, Klaus 14 Barrett, John W. 13 Styles, Vanessa 11 Dziuk, Gerhard 8 Stinner, Bjorn 5 Alphonse, Amal 5 Blowey, James F. 5 Fritz, Hans 5 Garcke, Harald 5 Kornhuber, Ralf 5 Ranner, Thomas 5 Schatzle, Reiner 5 Stuart, Andrew M. 4 Giga, Yoshikazu 4 Hinze, Michael 4 Ockendon, John R. 4 Tang, Qi 3 Brett, Charles 3 Chen, Xinfu 3 Copetti, Maria Inês M. 3 French, Donald A. 3 Friedman, Avner 3 Gardiner, Andrew R. 3 Herbert, Philip J. 3 Hobbs, Graham 3 Janovský, Vladimír 3 Mikelić, Andro 3 Venkataraman, Chandrasekhar 2 Briggs, Amy J. 2 Cahn, John W. 2 Claisse, J. R. 2 Dedner, Andreas S. 2 DiBenedetto, Emmanuele 2 Djurdjevac, Ana 2 Dunbar, Oliver R. A. 2 Hintermüller, Michael 2 Kashima, Yohei 2 Kostin, Ilya-Nikolaï 2 Larsson, Stig 2 Maier-Paape, Stanislaus 2 McKee, Sean 2 Smitheman, S. A. 2 Zheng, Songmu 1 Aitchison, Joyce M. 1 Bai, Fengshan 1 Barreira, Raquel 1 Chakrabarti, Roma 1 Chapman, Stephen Jonathan 1 Chen, Zhiming 1 Church, Lewis 1 Count, Brian M. 1 Croft, Wayne 1 Duncan, Andrew B. 1 Dunlop, Matthew M. 1 Eilks, C. 1 Fife, Paul C. 1 Gardiner, Andy 1 Gawron, Bernhard 1 Goto, Shun’ichi 1 Gräser, Carsten 1 Hatcher, Luke 1 Head, A. K. 1 Heine, Claus-Justus 1 Herrero, Miguel Ángel 1 Hoang, Viet Ha 1 Howison, Samuel Dexter 1 Huisken, Gerhard 1 King, John Robert 1 Ladds, Graham 1 Leslie, Frank M. 1 Leugering, Günter 1 Löbhard, Caroline 1 Lu, Bainian 1 Madzvamuse, Anotida 1 Mason, Colin J. 1 Matano, Hiroshi 1 Milner, Fabio Augusto 1 Miura, Tatsu-Hiko 1 Novick-Cohen, Amy 1 Paolini, Maurizio 1 Pavliotis, Grigorios A. 1 Sethian, James A. 1 Shillor, Meir 1 Sokołowski, Jan 1 Spence, Alastair 1 Stoth, Barbara E. E. 1 Styles, V. M. 1 Terra, Joana 1 Van Vleck, Erik S. 1 Welford, Richard 1 Weston, Cathryn 1 Wolf, Maren-Wanda 1 Zhao, Jennifer Jing all top 5 Serials 24 IMA Journal of Numerical Analysis 8 European Journal of Applied Mathematics 8 Interfaces and Free Boundaries 7 Numerische Mathematik 7 SIAM Journal on Numerical Analysis 7 SIAM Journal on Mathematical Analysis 7 Oberwolfach Reports 6 Mathematics of Computation 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Nonlinear Analysis. Theory, Methods & Applications 3 Archive for Rational Mechanics and Analysis 3 IMA Journal of Applied Mathematics 3 Journal of Computational Physics 3 Nonlinearity 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Inverse Problems 2 Journal of Mathematical Biology 2 Physica D 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Advances in Mathematical Sciences and Applications 2 Communications on Pure and Applied Analysis 2 Acta Numerica 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Journal of the Institute of Mathematics and its Applications 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 BIT 1 Hokkaido Mathematical Journal 1 Journal of Differential Equations 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 SIAM Journal on Control and Optimization 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Journal on Applied Mathematics 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 Computing and Visualization in Science 1 Optimization Methods & Software 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Portugaliae Mathematica. Nova Série 1 Milan Journal of Mathematics 1 Communications in Computational Physics 1 SIAM/ASA Journal on Uncertainty Quantification 1 Philosophical Transactions A. Royal Society of London 1 SMAI Journal of Computational Mathematics all top 5 Fields 122 Partial differential equations (35-XX) 93 Numerical analysis (65-XX) 32 Calculus of variations and optimal control; optimization (49-XX) 21 Fluid mechanics (76-XX) 21 Statistical mechanics, structure of matter (82-XX) 20 Mechanics of deformable solids (74-XX) 12 Classical thermodynamics, heat transfer (80-XX) 10 General and overarching topics; collections (00-XX) 10 Biology and other natural sciences (92-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Differential geometry (53-XX) 4 Optics, electromagnetic theory (78-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Ordinary differential equations (34-XX) 2 Computer science (68-XX) 2 Operations research, mathematical programming (90-XX) 2 Systems theory; control (93-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 135 Publications have been cited 3,428 times in 2,021 Documents Cited by ▼ Year ▼ On the Cahn-Hilliard equation. Zbl 0624.35048Elliott, Charles M.; Zheng, Songmu 214 1986 On the Cahn-Hilliard equation with degenerate mobility. Zbl 0856.35071Elliott, Charles M.; Garcke, Harald 197 1996 Finite element methods for surface PDEs. Zbl 1296.65156Dziuk, Gerhard; Elliott, Charles M. 186 2013 Computation of geometric partial differential equations and mean curvature flow. Zbl 1113.65097Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. 143 2005 Weak and variational methods for moving boundary problems. Zbl 0476.35080Elliott, C. M.; Ockendon, J. R. 135 1982 Finite elements on evolving surfaces. Zbl 1120.65102Dziuk, G.; Elliott, C. M. 124 2007 A second order splitting method for the Cahn-Hilliard equation. Zbl 0668.65097Elliott, C. M.; French, D. A.; Milner, F. A. 115 1989 The global dynamics of discrete semilinear parabolic equations. Zbl 0792.65066Elliott, C. M.; Stuart, A. M. 109 1993 Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0762.65074Copetti, M. I. M.; Elliott, C. M. 100 1992 Numerical studies of the Cahn-Hilliard equation for phase separation. Zbl 0632.65113Elliott, Charles M.; French, Donald A. 98 1987 The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. I: Mathematical analysis. Zbl 0797.35172Blowey, J. F.; Elliott, C. M. 86 1991 The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature. Zbl 0861.35039Cahn, J. W.; Elliott, C. M.; Novick-Cohen, A. 83 1996 Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation. Zbl 0762.65075Elliott, Charles M.; Larsson, Stig 81 1992 A nonconforming finite-element method for the two-dimensional Cahn- Hilliard equation. Zbl 0686.65086Elliott, Charles M.; French, Donald A. 81 1989 Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces. Zbl 0629.65118Barrett, John W.; Elliott, Charles M. 68 1987 Viscous Cahn-Hilliard equation. II: Analysis. Zbl 0855.35067Elliott, C. M.; Stuart, A. M. 64 1996 Modeling and computation of two phase geometric biomembranes using surface finite elements. Zbl 1425.74323Elliott, Charles M.; Stinner, Björn 55 2010 The viscous Cahn-Hilliard equation. I: Computations. Zbl 0818.35045Bai, F.; Elliott, C. M.; Gardiner, A.; Spence, A.; Stuart, A. M. 51 1995 The Cahn-Hilliard model for the kinetics of phase separation. Zbl 0692.73003Elliott, C. M. 49 1989 A variational inequality approach to Hele-Shaw flow with a moving boundary. Zbl 0455.76043Elliott, C. M.; Janovsky, V. 49 1981 The surface finite element method for pattern formation on evolving biological surfaces. Zbl 1234.92007Barreira, R.; Elliott, C. M.; Madzvamuse, A. 47 2011 The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. II: Numerical analysis. Zbl 0810.35158Blowey, J. F.; Elliott, C. M. 42 1992 Finite element analysis for a coupled bulk-surface partial differential equation. Zbl 1271.65138Elliott, Charles M.; Ranner, Thomas 41 2013 Finite element approximation of the Dirichlet problem using the boundary penalty method. Zbl 0614.65116Barrett, John W.; Elliott, Charles M. 34 1986 Shooting method for vortex solutions of a complex-valued Ginzburg-Landau equation. Zbl 0816.34003Chen, Xinfu; Elliott, Charles M.; Qi, Tang 33 1994 Numerical computation of advection and diffusion on evolving diffuse interfaces. Zbl 1241.65081Elliott, Charles M.; Stinner, Björn; Styles, Vanessa; Welford, Richard 33 2011 Error analysis of the enthalpy method for the Stefan problem. Zbl 0638.65088Elliott, C. M. 29 1987 Eulerian finite element method for parabolic PDEs on implicit surfaces. Zbl 1145.65073Dziuk, G.; Elliott, C. M. 27 2008 \(L^2\)-estimates for the evolving surface finite element method. Zbl 1269.65087Dziuk, Gerhard; Elliott, Charles M. 27 2013 An \(h\)-narrow band finite-element method for elliptic equations on implicit surfaces. Zbl 1191.65151Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.; Heine, Claus-Justus 26 2010 Curvature dependent phase boundary motion and parabolic double obstacle problems. Zbl 0794.35092Blowey, J. F.; Elliott, C. M. 26 1993 The mesa problem: diffusion patterns for \(u_ t=\nabla \cdot (u^ m\nabla u)\) as \(m\to +\infty\). Zbl 0655.35034Elliott, C. M.; Herrero, M. A.; King, J. R.; Ockendon, J. R. 25 1986 Existence results for diffusive surface motion laws. Zbl 0876.35050Elliott, Charles M.; Garcke, Harald 25 1997 Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. Zbl 1149.76027Eilks, C.; Elliott, C. M. 25 2008 Evolving surface finite element method for the Cahn-Hilliard equation. Zbl 1312.65159Elliott, Charles M.; Ranner, Thomas 24 2015 Numerical analysis of a model for phase separation of a multi-component alloy. Zbl 0857.65137Blowey, J. F.; Copetti, M. I. M.; Elliott, C. M. 23 1996 A finite element model for the time-dependent Joule heating problem. Zbl 0846.65047Elliott, Charles M.; Larsson, Stig 23 1995 Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equation. Zbl 0888.35047Elliott, C. M.; Kostin, I. N. 23 1996 Asymptotics for a parabolic double obstacle problem. Zbl 0814.35044Chen, Xinfu; Elliott, Charles M. 22 1994 An abstract framework for parabolic PDEs on evolving spaces. Zbl 1323.35103Alphonse, Amal; Elliott, Charles M.; Stinner, Björn 22 2015 A dynamic contact problem in thermoelasticity. Zbl 0818.73061Elliott, C. M.; Qi, Tang 21 1994 An Eulerian approach to transport and diffusion on evolving implicit surfaces. Zbl 1220.65132Dziuk, G.; Elliott, C. M. 21 2010 Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model. Zbl 0905.35084Chen, Zhiming; Elliott, C. M.; Qi, Tang 19 1998 Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Zbl 1081.35115Deckelnick, Klaus; Elliott, Charles M. 19 2004 On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick. Zbl 1433.65219M. Elliott, Charles; Fritz, Hans 19 2017 A surface phase field model for two-phase biological membranes. Zbl 1209.92003Elliott, Charles M.; Stinner, Björn 19 2010 Computation of two-phase biomembranes with phase dependent material parameters using surface finite elements. Zbl 1373.74089Elliott, Charles M.; Stinner, Björn 19 2013 A finite-element method for solving elliptic equations with Neumann data on a curved boundary using unfitted meshes. Zbl 0574.65121Barrett, John W.; Elliott, Charles M. 18 1984 Total flux estimates for a finite-element approximation of elliptic equations. Zbl 0619.65098Barrett, John W.; Elliott, Charles M. 17 1987 Convergence of numerical solutions to the Allen-Cahn equation. Zbl 0992.65096Chen, Xinfu; Elliott, Charlie M.; Gardiner, Andy; Zhao, Jennifer Jing 17 1998 Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface. Zbl 1200.35018Elliott, Charles M.; Stinner, Björn 17 2009 A one-dimensional quasi-static contact problem in linear thermoelasticity. Zbl 0779.73051Copetti, M. I. M.; Elliott, C. M. 17 1993 On the finite element approximation of an elliptic variational inequality arising from an implicit time discretization of the Stefan problem. Zbl 0469.65042Elliott, Charles M. 17 1981 An ALE ESFEM for solving PDEs on evolving surfaces. Zbl 1259.65147Elliott, Charles M.; Styles, Vanessa 17 2012 A fully discrete evolving surface finite element method. Zbl 1267.65128Dziuk, Gerhard; Elliott, Charles M. 17 2012 Percolation in gently sloping beaches. Zbl 0536.76085Aitchison, J. M.; Elliott, C. M.; Ockendon, J. R. 16 1983 A phase-field model with a double obstacle potential. Zbl 0809.35168Blowey, J. F.; Elliott, C. M. 16 1994 Unfitted finite element methods using bulk meshes for surface partial differential equations. Zbl 1307.65164Deckelnick, Klaus; Elliott, Charles M.; Ranner, Thomas 16 2014 On a variational inequality formulation of an electrochemical machining moving boundary problem and its approximation by the finite element method. Zbl 0428.49003Elliott, C. M. 15 1980 A free-boundary model for diffusion-induced grain boundary motion. Zbl 0986.35136Fife, P. C.; Cahn, J. W.; Elliott, C. M. 14 2001 Zeros of a complex Ginzburg-Landau order parameter with applications to superconductivity. Zbl 0817.35112Elliott, C. M.; Matano, H.; Qi, Tang 13 1994 Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087Elliott, Charles M.; Garcke, Harald 13 1997 On some linear parabolic PDEs on moving hypersurfaces. Zbl 1333.35306Alphonse, Amal; Elliott, Charles M.; Stinner, Björn 13 2015 Numerical diffusion-induced grain boundary motion. Zbl 0991.35095Deckelnick, K.; Elliott, C. M.; Styles, V. 12 2001 Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225Elliott, Charles M.; Garcke, Harald 12 1997 Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. Zbl 1366.35244Elliott, Charles M.; Ranner, Thomas; Venkataraman, Chandrasekhar 11 2017 Fully discrete finite element approximation for anisotropic surface diffusion of graphs. Zbl 1094.65098Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. 11 2005 Analysis of the TV regularization and \(H^{-1}\) fidelity model for decomposing an image into cartoon plus texture. Zbl 1148.35329Elliott, C. M.; Smitheman, S. A. 11 2007 Fixed mesh finite element approximations to a free boundary problem for an elliptic equation with an oblique derivative boundary condition. Zbl 0591.65072Barrett, John W.; Elliott, Charles M. 10 1985 Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces. Zbl 1058.65097Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. 10 2003 Long time asymptotics for forced curvature flow with applications to the motion of a superconducting vortex. Zbl 0909.35064Deckelnick, K.; Elliott, C. M.; Richardson, G. 10 1997 A finite-element analysis of critical-state models for type-II superconductivity in 3D. Zbl 1119.82046Elliott, Charles M.; Kashima, Yohei 10 2007 The limit of the anisotropic double-obstacle Allen-Cahn equation. Zbl 0865.35073Elliott, Charles M.; Schätzle, Reiner 10 1996 A variational approach to particles in lipid membranes. Zbl 1362.35311Elliott, Charles M.; Gräser, Carsten; Hobbs, Graham; Kornhuber, Ralf; Wolf, Maren-Wanda 10 2016 On the convergence of a one-step method for the numerical solution of an ordinary differential inclusion. Zbl 0598.65052Elliott, C. M. 9 1985 A practical finite element approximation of a semi-definite Neumann problem on a curved domain. Zbl 0617.65110Barrett, John W.; Elliott, Charles M. 9 1987 The free boundary of a flow in a porous body heated from its boundary. Zbl 0621.76101DiBenedetto, Emmanuele; Elliott, Charles M.; Friedman, Avner 9 1986 Dynamic boundary conditions for Hamilton–Jacobi equations. Zbl 1030.35115Elliott, C. M.; Giga, Y.; Goto, S. 9 2003 Losing a graph with surface diffusion. Zbl 0993.35042Elliott, Charles M.; Maier-Paape, Stanislaus 9 2001 Error analysis for an ALE evolving surface finite element method. Zbl 1318.65063Elliott, Charles M.; Venkataraman, Chandrasekhar 9 2015 Numerical analysis of the TV regularization and \(H^{-1}\) fidelity model for decomposing an image into cartoon plus texture. Zbl 1169.94003Elliott, C. M.; Smitheman, S. A. 8 2009 Finite-element approximation of elliptic equations with a Neumann or Robin condition on a curved boundary. Zbl 0658.65106Barrett, John W.; Elliott, Charles M. 8 1988 Approximation of curvature dependent interface motion. Zbl 0881.65131Elliott, C. M. 8 1997 A coupled ligand-receptor bulk-surface system on a moving domain: well posedness, regularity, and convergence to equilibrium. Zbl 1390.35144Alphonse, Amal; Elliott, Charles M.; Terra, Joana 8 2018 Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Zbl 1368.74039Elliott, Charles M.; Fritz, Hans; Hobbs, Graham 8 2017 Parameter identification problems in the modelling of cell motility. Zbl 1321.92043Croft, Wayne; Elliott, Charles M.; Ladds, Graham; Stinner, Björn; Venkataraman, Chandrasekhar; Weston, Cathryn 7 2015 Finite element error bounds for a curve shrinking with prescribed normal contact to a fixed boundary. Zbl 0921.65009Deckelnick, Klaus; Elliott, Charles M. 7 1998 Viscosity solutions of a degenerate parabolic-elliptic system arising in the mean-field theory of superconductivity. Zbl 0927.35117Elliott, Charles M.; Schätzle, Reiner; Stoth, Barbara E. E. 7 1998 Computations of bidirectional grain boundary dynamics in thin metallic films. Zbl 1020.82006Elliott, C. M.; Styles, V. 7 2003 Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean-curvature flow. Zbl 0873.35039Elliott, Charles M.; Paolini, Maurizio; Schätzle, Reiner 7 1996 The limit of the fully anisotropic double-obstacle Allen-Cahn equation in the nonsmooth case. Zbl 0870.35128Elliott, Charles M.; Schätzle, Reiner 7 1997 Global existence and stability of solutions to the phase field equations. Zbl 0733.35062Elliott, C. M.; Zheng, Songmu 6 1990 A finite element method on a fixed mesh for the Stefan problem with convection in a saturated porous medium. Zbl 0527.76096Barrett, J. W.; Elliott, C. M. 5 1982 Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient. Zbl 1339.65209Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa 5 2016 Numerical analysis of an inverse problem for the eikonal equation. Zbl 1244.65093Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa 5 2011 On algorithms with good mesh properties for problems with moving boundaries based on the harmonic map heat flow and the deturck trick. Zbl 1416.65324Elliott, Charles M.; Fritz, Hans 5 2016 Optimal control of elliptic PDEs at points. Zbl 1433.49041Brett, Charles; Dedner, Andreas; Elliott, Charles 5 2016 A Stefan problem on an evolving surface. Zbl 1353.35317Alphonse, Amal; Elliott, Charles M. 5 2015 Well-posedness of a fractional porous medium equation on an evolving surface. Zbl 1334.35365Alphonse, Amal; Elliott, Charles M. 5 2016 Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state. Zbl 1320.49016Brett, Charles; Elliott, Charles M.; Hintermüller, Michael; Löbhard, Caroline 4 2015 Domain formation via phase separation for spherical biomembranes with small deformations. Zbl 1479.35013Elliott, C. M.; Hatcher, L. 1 2021 A domain mapping approach for elliptic equations posed on random bulk and surface domains. Zbl 1452.65330Church, Lewis; Djurdjevac, Ana; Elliott, Charles M. 2 2020 Second order splitting of a class of fourth order PDEs with point constraints. Zbl 1446.65167Elliott, Charles M.; Herbert, Philip J. 1 2020 Reconciling Bayesian and perimeter regularization for binary inversion. Zbl 1455.62084Dunbar, Oliver R. A.; Dunlop, Matthew M.; Elliott, Charles M.; Hoang, Viet Ha; Stuart, Andrew M. 1 2020 Second order splitting for a class of fourth order equations. Zbl 1426.65175Elliott, Charles M.; Fritz, Hans; Hobbs, Graham 2 2019 Binary recovery via phase field regularization for first-arrival traveltime tomography. Zbl 1431.65153Dunbar, Oliver R. A.; Elliott, Charles M. 1 2019 A coupled ligand-receptor bulk-surface system on a moving domain: well posedness, regularity, and convergence to equilibrium. Zbl 1390.35144Alphonse, Amal; Elliott, Charles M.; Terra, Joana 8 2018 Evolving surface finite element methods for random advection-diffusion equations. Zbl 1407.65258Djurdjevac, Ana; Elliott, Charles M.; Kornhuber, Ralf; Ranner, Thomas 2 2018 On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick. Zbl 1433.65219M. Elliott, Charles; Fritz, Hans 19 2017 Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. Zbl 1366.35244Elliott, Charles M.; Ranner, Thomas; Venkataraman, Chandrasekhar 11 2017 Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Zbl 1368.74039Elliott, Charles M.; Fritz, Hans; Hobbs, Graham 8 2017 A variational approach to particles in lipid membranes. Zbl 1362.35311Elliott, Charles M.; Gräser, Carsten; Hobbs, Graham; Kornhuber, Ralf; Wolf, Maren-Wanda 10 2016 Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient. Zbl 1339.65209Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa 5 2016 On algorithms with good mesh properties for problems with moving boundaries based on the harmonic map heat flow and the deturck trick. Zbl 1416.65324Elliott, Charles M.; Fritz, Hans 5 2016 Optimal control of elliptic PDEs at points. Zbl 1433.49041Brett, Charles; Dedner, Andreas; Elliott, Charles 5 2016 Well-posedness of a fractional porous medium equation on an evolving surface. Zbl 1334.35365Alphonse, Amal; Elliott, Charles M. 5 2016 Evolving surface finite element method for the Cahn-Hilliard equation. Zbl 1312.65159Elliott, Charles M.; Ranner, Thomas 24 2015 An abstract framework for parabolic PDEs on evolving spaces. Zbl 1323.35103Alphonse, Amal; Elliott, Charles M.; Stinner, Björn 22 2015 On some linear parabolic PDEs on moving hypersurfaces. Zbl 1333.35306Alphonse, Amal; Elliott, Charles M.; Stinner, Björn 13 2015 Error analysis for an ALE evolving surface finite element method. Zbl 1318.65063Elliott, Charles M.; Venkataraman, Chandrasekhar 9 2015 Parameter identification problems in the modelling of cell motility. Zbl 1321.92043Croft, Wayne; Elliott, Charles M.; Ladds, Graham; Stinner, Björn; Venkataraman, Chandrasekhar; Weston, Cathryn 7 2015 A Stefan problem on an evolving surface. Zbl 1353.35317Alphonse, Amal; Elliott, Charles M. 5 2015 Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state. Zbl 1320.49016Brett, Charles; Elliott, Charles M.; Hintermüller, Michael; Löbhard, Caroline 4 2015 A multiscale analysis of diffusions on rapidly varying surfaces. Zbl 1311.35324Duncan, A. B.; Elliott, C. M.; Pavliotis, G. A.; Stuart, A. M. 2 2015 Unfitted finite element methods using bulk meshes for surface partial differential equations. Zbl 1307.65164Deckelnick, Klaus; Elliott, Charles M.; Ranner, Thomas 16 2014 Phase field methods for binary recovery. Zbl 1320.49024Brett, Charles; Elliott, Charles M.; Dedner, Andreas S. 3 2014 Finite element methods for surface PDEs. Zbl 1296.65156Dziuk, Gerhard; Elliott, Charles M. 186 2013 Finite element analysis for a coupled bulk-surface partial differential equation. Zbl 1271.65138Elliott, Charles M.; Ranner, Thomas 41 2013 \(L^2\)-estimates for the evolving surface finite element method. Zbl 1269.65087Dziuk, Gerhard; Elliott, Charles M. 27 2013 Computation of two-phase biomembranes with phase dependent material parameters using surface finite elements. Zbl 1373.74089Elliott, Charles M.; Stinner, Björn 19 2013 Interfaces and free boundaries: analysis, control and simulation. Abstracts from the workshop held March 24–30, 2013. Zbl 1349.00157 1 2013 An ALE ESFEM for solving PDEs on evolving surfaces. Zbl 1259.65147Elliott, Charles M.; Styles, Vanessa 17 2012 A fully discrete evolving surface finite element method. Zbl 1267.65128Dziuk, Gerhard; Elliott, Charles M. 17 2012 The surface finite element method for pattern formation on evolving biological surfaces. Zbl 1234.92007Barreira, R.; Elliott, C. M.; Madzvamuse, A. 47 2011 Numerical computation of advection and diffusion on evolving diffuse interfaces. Zbl 1241.65081Elliott, Charles M.; Stinner, Björn; Styles, Vanessa; Welford, Richard 33 2011 Numerical analysis of an inverse problem for the eikonal equation. Zbl 1244.65093Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa 5 2011 Geometric partial differential equations: theory, numerics and applications. Abstracts from the workshop held November 27 – December 3, 2011. Zbl 1349.00149 1 2011 Modeling and computation of two phase geometric biomembranes using surface finite elements. Zbl 1425.74323Elliott, Charles M.; Stinner, Björn 55 2010 An \(h\)-narrow band finite-element method for elliptic equations on implicit surfaces. Zbl 1191.65151Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.; Heine, Claus-Justus 26 2010 An Eulerian approach to transport and diffusion on evolving implicit surfaces. Zbl 1220.65132Dziuk, G.; Elliott, C. M. 21 2010 A surface phase field model for two-phase biological membranes. Zbl 1209.92003Elliott, Charles M.; Stinner, Björn 19 2010 Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface. Zbl 1200.35018Elliott, Charles M.; Stinner, Björn 17 2009 Numerical analysis of the TV regularization and \(H^{-1}\) fidelity model for decomposing an image into cartoon plus texture. Zbl 1169.94003Elliott, C. M.; Smitheman, S. A. 8 2009 Optimal control of the propagation of a graph in inhomogeneous media. Zbl 1282.49003Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa 4 2009 Eulerian finite element method for parabolic PDEs on implicit surfaces. Zbl 1145.65073Dziuk, G.; Elliott, C. M. 27 2008 Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. Zbl 1149.76027Eilks, C.; Elliott, C. M. 25 2008 Finite elements on evolving surfaces. Zbl 1120.65102Dziuk, G.; Elliott, C. M. 124 2007 Analysis of the TV regularization and \(H^{-1}\) fidelity model for decomposing an image into cartoon plus texture. Zbl 1148.35329Elliott, C. M.; Smitheman, S. A. 11 2007 A finite-element analysis of critical-state models for type-II superconductivity in 3D. Zbl 1119.82046Elliott, Charles M.; Kashima, Yohei 10 2007 Propagation of graphs in two-dimensional inhomogeneous media. Zbl 1126.65073Deckelnick, Klaus; Elliott, Charles M. 3 2006 On macroscopic critical state models of superconductivity in 3D. Zbl 1143.65379Elliott, Charles M.; Kashima, Yohei 1 2006 Computation of geometric partial differential equations and mean curvature flow. Zbl 1113.65097Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. 143 2005 Fully discrete finite element approximation for anisotropic surface diffusion of graphs. Zbl 1094.65098Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. 11 2005 Finite element analysis of a current density-electric field formulation of Bean’s model for superconductivity. Zbl 1100.78018Elliott, C. M.; Kay, D.; Styles, V. 2 2005 Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Zbl 1081.35115Deckelnick, Klaus; Elliott, Charles M. 19 2004 A finite element approximation of a variational inequality formulation of Bean’s model for superconductivity. Zbl 1071.82063Elliott, C. M.; Kay, D.; Styles, V. 4 2004 Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces. Zbl 1058.65097Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. 10 2003 Dynamic boundary conditions for Hamilton–Jacobi equations. Zbl 1030.35115Elliott, C. M.; Giga, Y.; Goto, S. 9 2003 Computations of bidirectional grain boundary dynamics in thin metallic films. Zbl 1020.82006Elliott, C. M.; Styles, V. 7 2003 Finite-difference approximation of a one-dimensional Hamilton-Jacobi/elliptic system arising in superconductivity. Zbl 0991.35092Briggs, A. J.; Claisse, J. R.; Elliott, C. M. 1 2002 A free-boundary model for diffusion-induced grain boundary motion. Zbl 0986.35136Fife, P. C.; Cahn, J. W.; Elliott, C. M. 14 2001 Numerical diffusion-induced grain boundary motion. Zbl 0991.35095Deckelnick, K.; Elliott, C. M.; Styles, V. 12 2001 Losing a graph with surface diffusion. Zbl 0993.35042Elliott, Charles M.; Maier-Paape, Stanislaus 9 2001 An existence and uniqueness result for a phase-filed model of diffusion-induced grain-boundary motion. Zbl 0989.35006Deckelnick, Klaus; Elliott, Charles M. 4 2001 Numerical analysis of a mean field model of superconducting vortices. Zbl 0984.82042Elliott, Charles M.; Styles, Vanessa 3 2001 Local and global existence results for anisotropic Hele-Shaw flows. Zbl 0922.76150Deckelnick, Klaus; Elliott, Charles M. 1 1999 Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model. Zbl 0905.35084Chen, Zhiming; Elliott, C. M.; Qi, Tang 19 1998 Convergence of numerical solutions to the Allen-Cahn equation. Zbl 0992.65096Chen, Xinfu; Elliott, Charlie M.; Gardiner, Andy; Zhao, Jennifer Jing 17 1998 Finite element error bounds for a curve shrinking with prescribed normal contact to a fixed boundary. Zbl 0921.65009Deckelnick, Klaus; Elliott, Charles M. 7 1998 Viscosity solutions of a degenerate parabolic-elliptic system arising in the mean-field theory of superconductivity. Zbl 0927.35117Elliott, Charles M.; Schätzle, Reiner; Stoth, Barbara E. E. 7 1998 Crystalline curvature flow of a graph in a variational setting. Zbl 0959.35168Elliott, Charles M.; Gardiner, Andrew R.; Schätzle, Reiner 4 1998 Existence results for diffusive surface motion laws. Zbl 0876.35050Elliott, Charles M.; Garcke, Harald 25 1997 Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087Elliott, Charles M.; Garcke, Harald 13 1997 Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225Elliott, Charles M.; Garcke, Harald 12 1997 Long time asymptotics for forced curvature flow with applications to the motion of a superconducting vortex. Zbl 0909.35064Deckelnick, K.; Elliott, C. M.; Richardson, G. 10 1997 Approximation of curvature dependent interface motion. Zbl 0881.65131Elliott, C. M. 8 1997 The limit of the fully anisotropic double-obstacle Allen-Cahn equation in the nonsmooth case. Zbl 0870.35128Elliott, Charles M.; Schätzle, Reiner 7 1997 Vortices, dislocations and line singularities in partial differential equations. Zbl 0886.00011 1 1997 On the Cahn-Hilliard equation with degenerate mobility. Zbl 0856.35071Elliott, Charles M.; Garcke, Harald 197 1996 The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature. Zbl 0861.35039Cahn, J. W.; Elliott, C. M.; Novick-Cohen, A. 83 1996 Viscous Cahn-Hilliard equation. II: Analysis. Zbl 0855.35067Elliott, C. M.; Stuart, A. M. 64 1996 Numerical analysis of a model for phase separation of a multi-component alloy. Zbl 0857.65137Blowey, J. F.; Copetti, M. I. M.; Elliott, C. M. 23 1996 Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equation. Zbl 0888.35047Elliott, C. M.; Kostin, I. N. 23 1996 The limit of the anisotropic double-obstacle Allen-Cahn equation. Zbl 0865.35073Elliott, Charles M.; Schätzle, Reiner 10 1996 Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean-curvature flow. Zbl 0873.35039Elliott, Charles M.; Paolini, Maurizio; Schätzle, Reiner 7 1996 The viscous Cahn-Hilliard equation. I: Computations. Zbl 0818.35045Bai, F.; Elliott, C. M.; Gardiner, A.; Spence, A.; Stuart, A. M. 51 1995 A finite element model for the time-dependent Joule heating problem. Zbl 0846.65047Elliott, Charles M.; Larsson, Stig 23 1995 Shooting method for vortex solutions of a complex-valued Ginzburg-Landau equation. Zbl 0816.34003Chen, Xinfu; Elliott, Charles M.; Qi, Tang 33 1994 Asymptotics for a parabolic double obstacle problem. Zbl 0814.35044Chen, Xinfu; Elliott, Charles M. 22 1994 A dynamic contact problem in thermoelasticity. Zbl 0818.73061Elliott, C. M.; Qi, Tang 21 1994 A phase-field model with a double obstacle potential. Zbl 0809.35168Blowey, J. F.; Elliott, C. M. 16 1994 Zeros of a complex Ginzburg-Landau order parameter with applications to superconductivity. Zbl 0817.35112Elliott, C. M.; Matano, H.; Qi, Tang 13 1994 One dimensional phase field computations. Zbl 0802.65123Elliott, C. M.; Gardiner, A. R. 3 1994 Mathematical and numerical analysis of a mean-field equation for the Ising model with Glauber dynamics. Zbl 0808.65139Elliott, C. M.; Gardiner, A. R.; Kostin, I.; Lu, Bainian 2 1994 The global dynamics of discrete semilinear parabolic equations. Zbl 0792.65066Elliott, C. M.; Stuart, A. M. 109 1993 Curvature dependent phase boundary motion and parabolic double obstacle problems. Zbl 0794.35092Blowey, J. F.; Elliott, C. M. 26 1993 A one-dimensional quasi-static contact problem in linear thermoelasticity. Zbl 0779.73051Copetti, M. I. M.; Elliott, C. M. 17 1993 Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0762.65074Copetti, M. I. M.; Elliott, C. M. 100 1992 Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation. Zbl 0762.65075Elliott, Charles M.; Larsson, Stig 81 1992 The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. II: Numerical analysis. Zbl 0810.35158Blowey, J. F.; Elliott, C. M. 42 1992 ...and 35 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,469 Authors 54 Garcke, Harald 51 Elliott, Charles M. 39 Nürnberg, Robert 34 Barrett, John W. 28 Colli, Pierluigi 23 Kim, Junseok 22 Miranville, Alain M. 21 Voigt, Axel 20 Madzvamuse, Anotida 19 Olshanskii, Maxim A. 17 Fan, Jishan 17 Hansbo, Peter 16 Gilardi, Gianni 16 Styles, Vanessa 16 Yang, Xiaofeng 15 Feng, Xinlong 15 Larson, Mats G. 15 Li, Buyang 15 Shen, Jie 14 Nochetto, Ricardo Horacio 14 Sprekels, Jürgen 13 Grasselli, Maurizio 13 Lam, Kei Fong 13 Wise, Steven M. 13 Zhao, Xiaopeng 12 Burman, Erik 12 Giga, Yoshikazu 12 King, John Robert 12 Lee, Hyun Geun 12 Sun, Shuyu 12 Wang, Cheng 11 Abels, Helmut 11 Deckelnick, Klaus 11 Liu, Chein-Shan 11 Novick-Cohen, Amy 11 Reusken, Arnold 11 Shin, Jaemin 11 Yin, Jingxue 10 Du, Qiang 10 Kou, Jisheng 10 Muñoz Rivera, Jaime Edilberto 10 Zelik, Sergey V. 9 Bao, Weizhu 9 Bartels, Sören 9 Burger, Martin 9 Feng, Xiaobing 9 Hinze, Michael 9 Kahle, Christian 9 Larsson, Stig 9 Stinner, Bjorn 9 Venkataraman, Chandrasekhar 9 Zeng, Jinping 8 Beneš, Michal 8 Chen, Wenbin 8 Cherfils, Laurence 8 Fukao, Takeshi 8 Grün, Günther 8 Gustafsson, Bjorn 8 Hughes, Thomas J. 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M. 7 Copetti, Maria Inês M. 7 Dai, Shibin 7 Deka, Bhupen 7 Fabrizio, Mauro 7 Fakih, Hussein 7 Frigeri, Sergio 7 Hintermüller, Michael 7 Jia, Hongen 7 Ju, Lili 7 Kenmochi, Nobuyuki 7 Kim, Inwon Christina 7 Li, Xiaolin 7 Verdi, Claudio 7 Zhao, Quan 7 Zhou, Yong 6 Bates, Peter W. 6 Bonfoh, Ahmed S. 6 Bretin, Elie 6 Dehghan Takht Fooladi, Mehdi 6 Duan, Ning 6 Kovács, Balázs 6 Kovács, Mihály 6 Lehrenfeld, Christoph 6 Li, Yibao 6 Li, Yukun 6 Liu, Chun 6 Liu, Qiang 6 Lubich, Christian 6 Mackenzie, John A. 6 Pawlow, Irena 6 Pierre, Morgan 6 Rabczuk, Timon ...and 2,369 more Authors all top 5 Cited in 295 Serials 133 Journal of Computational Physics 81 Computer Methods in Applied Mechanics and Engineering 70 Numerische Mathematik 69 Journal of Scientific Computing 68 Journal of Computational and Applied Mathematics 60 Computers & Mathematics with Applications 54 Journal of Mathematical Analysis and Applications 50 Journal of Differential Equations 49 SIAM Journal on Numerical Analysis 43 Mathematics of Computation 40 Applied Numerical Mathematics 36 Nonlinear Analysis. 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Zeitschrift für Angewandte Mathematik und Mechanik ...and 195 more Serials all top 5 Cited in 48 Fields 1,358 Partial differential equations (35-XX) 1,018 Numerical analysis (65-XX) 410 Fluid mechanics (76-XX) 260 Mechanics of deformable solids (74-XX) 174 Statistical mechanics, structure of matter (82-XX) 164 Calculus of variations and optimal control; optimization (49-XX) 160 Classical thermodynamics, heat transfer (80-XX) 132 Biology and other natural sciences (92-XX) 85 Differential geometry (53-XX) 76 Global analysis, analysis on manifolds (58-XX) 71 Dynamical systems and ergodic theory (37-XX) 55 Probability theory and stochastic processes (60-XX) 34 Optics, electromagnetic theory (78-XX) 34 Operations research, mathematical programming (90-XX) 32 Ordinary differential equations (34-XX) 30 Integral equations (45-XX) 30 Operator theory (47-XX) 28 Computer science (68-XX) 24 Information and communication theory, circuits (94-XX) 21 Geophysics (86-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 Approximations and expansions (41-XX) 15 Systems theory; control (93-XX) 14 Real functions (26-XX) 14 Potential theory (31-XX) 12 Functional analysis (46-XX) 12 Statistics (62-XX) 11 Quantum theory (81-XX) 9 Functions of a complex variable (30-XX) 6 Mechanics of particles and systems (70-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 3 Combinatorics (05-XX) 3 Special functions (33-XX) 3 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Measure and integration (28-XX) 2 Difference and functional equations (39-XX) 2 Convex and discrete geometry (52-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Algebraic topology (55-XX) 1 Mathematics education (97-XX) Citations by Year