×

Elliott, Charles M.

Compute Distance To:
Author ID: elliott.charles-m Recent zbMATH articles by "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
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

Publications by Year

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 0624.35048
Elliott, Charles M.; Zheng, Songmu
214
1986
On the Cahn-Hilliard equation with degenerate mobility. Zbl 0856.35071
Elliott, Charles M.; Garcke, Harald
197
1996
Finite element methods for surface PDEs. Zbl 1296.65156
Dziuk, Gerhard; Elliott, Charles M.
186
2013
Computation of geometric partial differential equations and mean curvature flow. Zbl 1113.65097
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.
143
2005
Weak and variational methods for moving boundary problems. Zbl 0476.35080
Elliott, C. M.; Ockendon, J. R.
135
1982
Finite elements on evolving surfaces. Zbl 1120.65102
Dziuk, G.; Elliott, C. M.
124
2007
A second order splitting method for the Cahn-Hilliard equation. Zbl 0668.65097
Elliott, C. M.; French, D. A.; Milner, F. A.
115
1989
The global dynamics of discrete semilinear parabolic equations. Zbl 0792.65066
Elliott, C. M.; Stuart, A. M.
109
1993
Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0762.65074
Copetti, M. I. M.; Elliott, C. M.
100
1992
Numerical studies of the Cahn-Hilliard equation for phase separation. Zbl 0632.65113
Elliott, Charles M.; French, Donald A.
98
1987
The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. I: Mathematical analysis. Zbl 0797.35172
Blowey, 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 0861.35039
Cahn, 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 0762.65075
Elliott, Charles M.; Larsson, Stig
81
1992
A nonconforming finite-element method for the two-dimensional Cahn- Hilliard equation. Zbl 0686.65086
Elliott, Charles M.; French, Donald A.
81
1989
Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces. Zbl 0629.65118
Barrett, John W.; Elliott, Charles M.
68
1987
Viscous Cahn-Hilliard equation. II: Analysis. Zbl 0855.35067
Elliott, C. M.; Stuart, A. M.
64
1996
Modeling and computation of two phase geometric biomembranes using surface finite elements. Zbl 1425.74323
Elliott, Charles M.; Stinner, Björn
55
2010
The viscous Cahn-Hilliard equation. I: Computations. Zbl 0818.35045
Bai, F.; Elliott, C. M.; Gardiner, A.; Spence, A.; Stuart, A. M.
51
1995
The Cahn-Hilliard model for the kinetics of phase separation. Zbl 0692.73003
Elliott, C. M.
49
1989
A variational inequality approach to Hele-Shaw flow with a moving boundary. Zbl 0455.76043
Elliott, C. M.; Janovsky, V.
49
1981
The surface finite element method for pattern formation on evolving biological surfaces. Zbl 1234.92007
Barreira, 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 0810.35158
Blowey, J. F.; Elliott, C. M.
42
1992
Finite element analysis for a coupled bulk-surface partial differential equation. Zbl 1271.65138
Elliott, Charles M.; Ranner, Thomas
41
2013
Finite element approximation of the Dirichlet problem using the boundary penalty method. Zbl 0614.65116
Barrett, John W.; Elliott, Charles M.
34
1986
Shooting method for vortex solutions of a complex-valued Ginzburg-Landau equation. Zbl 0816.34003
Chen, Xinfu; Elliott, Charles M.; Qi, Tang
33
1994
Numerical computation of advection and diffusion on evolving diffuse interfaces. Zbl 1241.65081
Elliott, Charles M.; Stinner, Björn; Styles, Vanessa; Welford, Richard
33
2011
Error analysis of the enthalpy method for the Stefan problem. Zbl 0638.65088
Elliott, C. M.
29
1987
Eulerian finite element method for parabolic PDEs on implicit surfaces. Zbl 1145.65073
Dziuk, G.; Elliott, C. M.
27
2008
\(L^2\)-estimates for the evolving surface finite element method. Zbl 1269.65087
Dziuk, Gerhard; Elliott, Charles M.
27
2013
An \(h\)-narrow band finite-element method for elliptic equations on implicit surfaces. Zbl 1191.65151
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.; Heine, Claus-Justus
26
2010
Curvature dependent phase boundary motion and parabolic double obstacle problems. Zbl 0794.35092
Blowey, 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 0655.35034
Elliott, C. M.; Herrero, M. A.; King, J. R.; Ockendon, J. R.
25
1986
Existence results for diffusive surface motion laws. Zbl 0876.35050
Elliott, Charles M.; Garcke, Harald
25
1997
Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. Zbl 1149.76027
Eilks, C.; Elliott, C. M.
25
2008
Evolving surface finite element method for the Cahn-Hilliard equation. Zbl 1312.65159
Elliott, Charles M.; Ranner, Thomas
24
2015
Numerical analysis of a model for phase separation of a multi-component alloy. Zbl 0857.65137
Blowey, J. F.; Copetti, M. I. M.; Elliott, C. M.
23
1996
A finite element model for the time-dependent Joule heating problem. Zbl 0846.65047
Elliott, Charles M.; Larsson, Stig
23
1995
Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equation. Zbl 0888.35047
Elliott, C. M.; Kostin, I. N.
23
1996
Asymptotics for a parabolic double obstacle problem. Zbl 0814.35044
Chen, Xinfu; Elliott, Charles M.
22
1994
An abstract framework for parabolic PDEs on evolving spaces. Zbl 1323.35103
Alphonse, Amal; Elliott, Charles M.; Stinner, Björn
22
2015
A dynamic contact problem in thermoelasticity. Zbl 0818.73061
Elliott, C. M.; Qi, Tang
21
1994
An Eulerian approach to transport and diffusion on evolving implicit surfaces. Zbl 1220.65132
Dziuk, G.; Elliott, C. M.
21
2010
Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model. Zbl 0905.35084
Chen, Zhiming; Elliott, C. M.; Qi, Tang
19
1998
Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Zbl 1081.35115
Deckelnick, 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 1433.65219
M. Elliott, Charles; Fritz, Hans
19
2017
A surface phase field model for two-phase biological membranes. Zbl 1209.92003
Elliott, Charles M.; Stinner, Björn
19
2010
Computation of two-phase biomembranes with phase dependent material parameters using surface finite elements. Zbl 1373.74089
Elliott, 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 0574.65121
Barrett, John W.; Elliott, Charles M.
18
1984
Total flux estimates for a finite-element approximation of elliptic equations. Zbl 0619.65098
Barrett, John W.; Elliott, Charles M.
17
1987
Convergence of numerical solutions to the Allen-Cahn equation. Zbl 0992.65096
Chen, 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 1200.35018
Elliott, Charles M.; Stinner, Björn
17
2009
A one-dimensional quasi-static contact problem in linear thermoelasticity. Zbl 0779.73051
Copetti, 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 0469.65042
Elliott, Charles M.
17
1981
An ALE ESFEM for solving PDEs on evolving surfaces. Zbl 1259.65147
Elliott, Charles M.; Styles, Vanessa
17
2012
A fully discrete evolving surface finite element method. Zbl 1267.65128
Dziuk, Gerhard; Elliott, Charles M.
17
2012
Percolation in gently sloping beaches. Zbl 0536.76085
Aitchison, J. M.; Elliott, C. M.; Ockendon, J. R.
16
1983
A phase-field model with a double obstacle potential. Zbl 0809.35168
Blowey, J. F.; Elliott, C. M.
16
1994
Unfitted finite element methods using bulk meshes for surface partial differential equations. Zbl 1307.65164
Deckelnick, 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 0428.49003
Elliott, C. M.
15
1980
A free-boundary model for diffusion-induced grain boundary motion. Zbl 0986.35136
Fife, P. C.; Cahn, J. W.; Elliott, C. M.
14
2001
Zeros of a complex Ginzburg-Landau order parameter with applications to superconductivity. Zbl 0817.35112
Elliott, C. M.; Matano, H.; Qi, Tang
13
1994
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087
Elliott, Charles M.; Garcke, Harald
13
1997
On some linear parabolic PDEs on moving hypersurfaces. Zbl 1333.35306
Alphonse, Amal; Elliott, Charles M.; Stinner, Björn
13
2015
Numerical diffusion-induced grain boundary motion. Zbl 0991.35095
Deckelnick, K.; Elliott, C. M.; Styles, V.
12
2001
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225
Elliott, Charles M.; Garcke, Harald
12
1997
Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. Zbl 1366.35244
Elliott, Charles M.; Ranner, Thomas; Venkataraman, Chandrasekhar
11
2017
Fully discrete finite element approximation for anisotropic surface diffusion of graphs. Zbl 1094.65098
Deckelnick, 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 1148.35329
Elliott, 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 0591.65072
Barrett, John W.; Elliott, Charles M.
10
1985
Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces. Zbl 1058.65097
Deckelnick, 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 0909.35064
Deckelnick, K.; Elliott, C. M.; Richardson, G.
10
1997
A finite-element analysis of critical-state models for type-II superconductivity in 3D. Zbl 1119.82046
Elliott, Charles M.; Kashima, Yohei
10
2007
The limit of the anisotropic double-obstacle Allen-Cahn equation. Zbl 0865.35073
Elliott, Charles M.; Schätzle, Reiner
10
1996
A variational approach to particles in lipid membranes. Zbl 1362.35311
Elliott, 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 0598.65052
Elliott, C. M.
9
1985
A practical finite element approximation of a semi-definite Neumann problem on a curved domain. Zbl 0617.65110
Barrett, John W.; Elliott, Charles M.
9
1987
The free boundary of a flow in a porous body heated from its boundary. Zbl 0621.76101
DiBenedetto, Emmanuele; Elliott, Charles M.; Friedman, Avner
9
1986
Dynamic boundary conditions for Hamilton–Jacobi equations. Zbl 1030.35115
Elliott, C. M.; Giga, Y.; Goto, S.
9
2003
Losing a graph with surface diffusion. Zbl 0993.35042
Elliott, Charles M.; Maier-Paape, Stanislaus
9
2001
Error analysis for an ALE evolving surface finite element method. Zbl 1318.65063
Elliott, 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 1169.94003
Elliott, C. M.; Smitheman, S. A.
8
2009
Finite-element approximation of elliptic equations with a Neumann or Robin condition on a curved boundary. Zbl 0658.65106
Barrett, John W.; Elliott, Charles M.
8
1988
Approximation of curvature dependent interface motion. Zbl 0881.65131
Elliott, C. M.
8
1997
A coupled ligand-receptor bulk-surface system on a moving domain: well posedness, regularity, and convergence to equilibrium. Zbl 1390.35144
Alphonse, Amal; Elliott, Charles M.; Terra, Joana
8
2018
Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Zbl 1368.74039
Elliott, Charles M.; Fritz, Hans; Hobbs, Graham
8
2017
Parameter identification problems in the modelling of cell motility. Zbl 1321.92043
Croft, 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 0921.65009
Deckelnick, Klaus; Elliott, Charles M.
7
1998
Viscosity solutions of a degenerate parabolic-elliptic system arising in the mean-field theory of superconductivity. Zbl 0927.35117
Elliott, Charles M.; Schätzle, Reiner; Stoth, Barbara E. E.
7
1998
Computations of bidirectional grain boundary dynamics in thin metallic films. Zbl 1020.82006
Elliott, C. M.; Styles, V.
7
2003
Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean-curvature flow. Zbl 0873.35039
Elliott, Charles M.; Paolini, Maurizio; Schätzle, Reiner
7
1996
The limit of the fully anisotropic double-obstacle Allen-Cahn equation in the nonsmooth case. Zbl 0870.35128
Elliott, Charles M.; Schätzle, Reiner
7
1997
Global existence and stability of solutions to the phase field equations. Zbl 0733.35062
Elliott, 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 0527.76096
Barrett, J. W.; Elliott, C. M.
5
1982
Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient. Zbl 1339.65209
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa
5
2016
Numerical analysis of an inverse problem for the eikonal equation. Zbl 1244.65093
Deckelnick, 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 1416.65324
Elliott, Charles M.; Fritz, Hans
5
2016
Optimal control of elliptic PDEs at points. Zbl 1433.49041
Brett, Charles; Dedner, Andreas; Elliott, Charles
5
2016
A Stefan problem on an evolving surface. Zbl 1353.35317
Alphonse, Amal; Elliott, Charles M.
5
2015
Well-posedness of a fractional porous medium equation on an evolving surface. Zbl 1334.35365
Alphonse, Amal; Elliott, Charles M.
5
2016
Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state. Zbl 1320.49016
Brett, Charles; Elliott, Charles M.; Hintermüller, Michael; Löbhard, Caroline
4
2015
Domain formation via phase separation for spherical biomembranes with small deformations. Zbl 1479.35013
Elliott, C. M.; Hatcher, L.
1
2021
A domain mapping approach for elliptic equations posed on random bulk and surface domains. Zbl 1452.65330
Church, Lewis; Djurdjevac, Ana; Elliott, Charles M.
2
2020
Second order splitting of a class of fourth order PDEs with point constraints. Zbl 1446.65167
Elliott, Charles M.; Herbert, Philip J.
1
2020
Reconciling Bayesian and perimeter regularization for binary inversion. Zbl 1455.62084
Dunbar, 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 1426.65175
Elliott, Charles M.; Fritz, Hans; Hobbs, Graham
2
2019
Binary recovery via phase field regularization for first-arrival traveltime tomography. Zbl 1431.65153
Dunbar, 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 1390.35144
Alphonse, Amal; Elliott, Charles M.; Terra, Joana
8
2018
Evolving surface finite element methods for random advection-diffusion equations. Zbl 1407.65258
Djurdjevac, 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 1433.65219
M. Elliott, Charles; Fritz, Hans
19
2017
Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. Zbl 1366.35244
Elliott, Charles M.; Ranner, Thomas; Venkataraman, Chandrasekhar
11
2017
Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Zbl 1368.74039
Elliott, Charles M.; Fritz, Hans; Hobbs, Graham
8
2017
A variational approach to particles in lipid membranes. Zbl 1362.35311
Elliott, 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 1339.65209
Deckelnick, 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 1416.65324
Elliott, Charles M.; Fritz, Hans
5
2016
Optimal control of elliptic PDEs at points. Zbl 1433.49041
Brett, Charles; Dedner, Andreas; Elliott, Charles
5
2016
Well-posedness of a fractional porous medium equation on an evolving surface. Zbl 1334.35365
Alphonse, Amal; Elliott, Charles M.
5
2016
Evolving surface finite element method for the Cahn-Hilliard equation. Zbl 1312.65159
Elliott, Charles M.; Ranner, Thomas
24
2015
An abstract framework for parabolic PDEs on evolving spaces. Zbl 1323.35103
Alphonse, Amal; Elliott, Charles M.; Stinner, Björn
22
2015
On some linear parabolic PDEs on moving hypersurfaces. Zbl 1333.35306
Alphonse, Amal; Elliott, Charles M.; Stinner, Björn
13
2015
Error analysis for an ALE evolving surface finite element method. Zbl 1318.65063
Elliott, Charles M.; Venkataraman, Chandrasekhar
9
2015
Parameter identification problems in the modelling of cell motility. Zbl 1321.92043
Croft, Wayne; Elliott, Charles M.; Ladds, Graham; Stinner, Björn; Venkataraman, Chandrasekhar; Weston, Cathryn
7
2015
A Stefan problem on an evolving surface. Zbl 1353.35317
Alphonse, Amal; Elliott, Charles M.
5
2015
Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state. Zbl 1320.49016
Brett, Charles; Elliott, Charles M.; Hintermüller, Michael; Löbhard, Caroline
4
2015
A multiscale analysis of diffusions on rapidly varying surfaces. Zbl 1311.35324
Duncan, 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 1307.65164
Deckelnick, Klaus; Elliott, Charles M.; Ranner, Thomas
16
2014
Phase field methods for binary recovery. Zbl 1320.49024
Brett, Charles; Elliott, Charles M.; Dedner, Andreas S.
3
2014
Finite element methods for surface PDEs. Zbl 1296.65156
Dziuk, Gerhard; Elliott, Charles M.
186
2013
Finite element analysis for a coupled bulk-surface partial differential equation. Zbl 1271.65138
Elliott, Charles M.; Ranner, Thomas
41
2013
\(L^2\)-estimates for the evolving surface finite element method. Zbl 1269.65087
Dziuk, Gerhard; Elliott, Charles M.
27
2013
Computation of two-phase biomembranes with phase dependent material parameters using surface finite elements. Zbl 1373.74089
Elliott, 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 1259.65147
Elliott, Charles M.; Styles, Vanessa
17
2012
A fully discrete evolving surface finite element method. Zbl 1267.65128
Dziuk, Gerhard; Elliott, Charles M.
17
2012
The surface finite element method for pattern formation on evolving biological surfaces. Zbl 1234.92007
Barreira, R.; Elliott, C. M.; Madzvamuse, A.
47
2011
Numerical computation of advection and diffusion on evolving diffuse interfaces. Zbl 1241.65081
Elliott, Charles M.; Stinner, Björn; Styles, Vanessa; Welford, Richard
33
2011
Numerical analysis of an inverse problem for the eikonal equation. Zbl 1244.65093
Deckelnick, 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 1425.74323
Elliott, Charles M.; Stinner, Björn
55
2010
An \(h\)-narrow band finite-element method for elliptic equations on implicit surfaces. Zbl 1191.65151
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.; Heine, Claus-Justus
26
2010
An Eulerian approach to transport and diffusion on evolving implicit surfaces. Zbl 1220.65132
Dziuk, G.; Elliott, C. M.
21
2010
A surface phase field model for two-phase biological membranes. Zbl 1209.92003
Elliott, Charles M.; Stinner, Björn
19
2010
Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface. Zbl 1200.35018
Elliott, 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 1169.94003
Elliott, C. M.; Smitheman, S. A.
8
2009
Optimal control of the propagation of a graph in inhomogeneous media. Zbl 1282.49003
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa
4
2009
Eulerian finite element method for parabolic PDEs on implicit surfaces. Zbl 1145.65073
Dziuk, G.; Elliott, C. M.
27
2008
Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. Zbl 1149.76027
Eilks, C.; Elliott, C. M.
25
2008
Finite elements on evolving surfaces. Zbl 1120.65102
Dziuk, 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 1148.35329
Elliott, C. M.; Smitheman, S. A.
11
2007
A finite-element analysis of critical-state models for type-II superconductivity in 3D. Zbl 1119.82046
Elliott, Charles M.; Kashima, Yohei
10
2007
Propagation of graphs in two-dimensional inhomogeneous media. Zbl 1126.65073
Deckelnick, Klaus; Elliott, Charles M.
3
2006
On macroscopic critical state models of superconductivity in 3D. Zbl 1143.65379
Elliott, Charles M.; Kashima, Yohei
1
2006
Computation of geometric partial differential equations and mean curvature flow. Zbl 1113.65097
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.
143
2005
Fully discrete finite element approximation for anisotropic surface diffusion of graphs. Zbl 1094.65098
Deckelnick, 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 1100.78018
Elliott, C. M.; Kay, D.; Styles, V.
2
2005
Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Zbl 1081.35115
Deckelnick, Klaus; Elliott, Charles M.
19
2004
A finite element approximation of a variational inequality formulation of Bean’s model for superconductivity. Zbl 1071.82063
Elliott, C. M.; Kay, D.; Styles, V.
4
2004
Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces. Zbl 1058.65097
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.
10
2003
Dynamic boundary conditions for Hamilton–Jacobi equations. Zbl 1030.35115
Elliott, C. M.; Giga, Y.; Goto, S.
9
2003
Computations of bidirectional grain boundary dynamics in thin metallic films. Zbl 1020.82006
Elliott, C. M.; Styles, V.
7
2003
Finite-difference approximation of a one-dimensional Hamilton-Jacobi/elliptic system arising in superconductivity. Zbl 0991.35092
Briggs, A. J.; Claisse, J. R.; Elliott, C. M.
1
2002
A free-boundary model for diffusion-induced grain boundary motion. Zbl 0986.35136
Fife, P. C.; Cahn, J. W.; Elliott, C. M.
14
2001
Numerical diffusion-induced grain boundary motion. Zbl 0991.35095
Deckelnick, K.; Elliott, C. M.; Styles, V.
12
2001
Losing a graph with surface diffusion. Zbl 0993.35042
Elliott, Charles M.; Maier-Paape, Stanislaus
9
2001
An existence and uniqueness result for a phase-filed model of diffusion-induced grain-boundary motion. Zbl 0989.35006
Deckelnick, Klaus; Elliott, Charles M.
4
2001
Numerical analysis of a mean field model of superconducting vortices. Zbl 0984.82042
Elliott, Charles M.; Styles, Vanessa
3
2001
Local and global existence results for anisotropic Hele-Shaw flows. Zbl 0922.76150
Deckelnick, Klaus; Elliott, Charles M.
1
1999
Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model. Zbl 0905.35084
Chen, Zhiming; Elliott, C. M.; Qi, Tang
19
1998
Convergence of numerical solutions to the Allen-Cahn equation. Zbl 0992.65096
Chen, 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 0921.65009
Deckelnick, Klaus; Elliott, Charles M.
7
1998
Viscosity solutions of a degenerate parabolic-elliptic system arising in the mean-field theory of superconductivity. Zbl 0927.35117
Elliott, Charles M.; Schätzle, Reiner; Stoth, Barbara E. E.
7
1998
Crystalline curvature flow of a graph in a variational setting. Zbl 0959.35168
Elliott, Charles M.; Gardiner, Andrew R.; Schätzle, Reiner
4
1998
Existence results for diffusive surface motion laws. Zbl 0876.35050
Elliott, Charles M.; Garcke, Harald
25
1997
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087
Elliott, Charles M.; Garcke, Harald
13
1997
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225
Elliott, Charles M.; Garcke, Harald
12
1997
Long time asymptotics for forced curvature flow with applications to the motion of a superconducting vortex. Zbl 0909.35064
Deckelnick, K.; Elliott, C. M.; Richardson, G.
10
1997
Approximation of curvature dependent interface motion. Zbl 0881.65131
Elliott, C. M.
8
1997
The limit of the fully anisotropic double-obstacle Allen-Cahn equation in the nonsmooth case. Zbl 0870.35128
Elliott, 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 0856.35071
Elliott, 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 0861.35039
Cahn, J. W.; Elliott, C. M.; Novick-Cohen, A.
83
1996
Viscous Cahn-Hilliard equation. II: Analysis. Zbl 0855.35067
Elliott, C. M.; Stuart, A. M.
64
1996
Numerical analysis of a model for phase separation of a multi-component alloy. Zbl 0857.65137
Blowey, 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 0888.35047
Elliott, C. M.; Kostin, I. N.
23
1996
The limit of the anisotropic double-obstacle Allen-Cahn equation. Zbl 0865.35073
Elliott, Charles M.; Schätzle, Reiner
10
1996
Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean-curvature flow. Zbl 0873.35039
Elliott, Charles M.; Paolini, Maurizio; Schätzle, Reiner
7
1996
The viscous Cahn-Hilliard equation. I: Computations. Zbl 0818.35045
Bai, 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 0846.65047
Elliott, Charles M.; Larsson, Stig
23
1995
Shooting method for vortex solutions of a complex-valued Ginzburg-Landau equation. Zbl 0816.34003
Chen, Xinfu; Elliott, Charles M.; Qi, Tang
33
1994
Asymptotics for a parabolic double obstacle problem. Zbl 0814.35044
Chen, Xinfu; Elliott, Charles M.
22
1994
A dynamic contact problem in thermoelasticity. Zbl 0818.73061
Elliott, C. M.; Qi, Tang
21
1994
A phase-field model with a double obstacle potential. Zbl 0809.35168
Blowey, J. F.; Elliott, C. M.
16
1994
Zeros of a complex Ginzburg-Landau order parameter with applications to superconductivity. Zbl 0817.35112
Elliott, C. M.; Matano, H.; Qi, Tang
13
1994
One dimensional phase field computations. Zbl 0802.65123
Elliott, C. M.; Gardiner, A. R.
3
1994
Mathematical and numerical analysis of a mean-field equation for the Ising model with Glauber dynamics. Zbl 0808.65139
Elliott, C. M.; Gardiner, A. R.; Kostin, I.; Lu, Bainian
2
1994
The global dynamics of discrete semilinear parabolic equations. Zbl 0792.65066
Elliott, C. M.; Stuart, A. M.
109
1993
Curvature dependent phase boundary motion and parabolic double obstacle problems. Zbl 0794.35092
Blowey, J. F.; Elliott, C. M.
26
1993
A one-dimensional quasi-static contact problem in linear thermoelasticity. Zbl 0779.73051
Copetti, M. I. M.; Elliott, C. M.
17
1993
Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0762.65074
Copetti, 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 0762.65075
Elliott, Charles M.; Larsson, Stig
81
1992
The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. II: Numerical analysis. Zbl 0810.35158
Blowey, J. F.; Elliott, C. M.
42
1992
...and 35 more Documents
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. R.
8 Lowengrub, John Samuel
8 Nitschke, Ingo
8 Rocca, Elisabetta
8 Scarpa, Luca
8 Wheeler, Glen E.
8 Xiao, Xufeng
8 Xu, Yan
7 Blank, Luise
7 Choo, S. 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. Theory, Methods & Applications. Series A: Theory and Methods
36 SIAM Journal on Scientific Computing
34 Applied Mathematics and Computation
31 European Journal of Applied Mathematics
28 Physica D
28 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
27 Archive for Rational Mechanics and Analysis
24 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
22 Applicable Analysis
20 Numerical Methods for Partial Differential Equations
20 Nonlinear Analysis. Theory, Methods & Applications
19 Mathematical Methods in the Applied Sciences
19 Communications in Computational Physics
17 Applied Mathematics Letters
16 SIAM Journal on Mathematical Analysis
16 Discrete and Continuous Dynamical Systems
14 Journal of Mathematical Physics
14 ZAMP. Zeitschrift für angewandte Mathematik und Physik
14 Nonlinear Analysis. Real World Applications
13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
13 Calculus of Variations and Partial Differential Equations
12 Applied Mathematics and Optimization
12 Numerical Functional Analysis and Optimization
12 Japan Journal of Industrial and Applied Mathematics
12 NoDEA. Nonlinear Differential Equations and Applications
12 Advances in Computational Mathematics
12 Discrete and Continuous Dynamical Systems. Series B
12 Communications on Pure and Applied Analysis
11 Journal of Fluid Mechanics
11 Computational Methods in Applied Mathematics
10 Journal of Mathematical Biology
10 Annali di Matematica Pura ed Applicata. Serie Quarta
10 BIT
10 Applied Mathematical Modelling
10 Communications in Partial Differential Equations
10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
10 SIAM Journal on Applied Mathematics
10 Computational and Applied Mathematics
10 Engineering Analysis with Boundary Elements
10 Interfaces and Free Boundaries
10 Multiscale Modeling & Simulation
9 SIAM Journal on Control and Optimization
9 Transactions of the American Mathematical Society
9 Computational Mechanics
9 Numerical Algorithms
9 Journal of Mathematical Imaging and Vision
8 International Journal for Numerical Methods in Engineering
8 Quarterly of Applied Mathematics
8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
8 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
8 Discrete and Continuous Dynamical Systems. Series S
7 Computers and Fluids
7 Inverse Problems
7 Calcolo
7 RAIRO. Modélisation Mathématique et Analyse Numérique
7 Mathematical and Computer Modelling
7 Asymptotic Analysis
7 Applications of Mathematics
7 International Journal of Computer Mathematics
7 Communications in Nonlinear Science and Numerical Simulation
7 SIAM Journal on Applied Dynamical Systems
7 SIAM Journal on Imaging Sciences
7 SIAM/ASA Journal on Uncertainty Quantification
6 Journal of Statistical Physics
6 Bulletin of Mathematical Biology
6 Mathematics and Computers in Simulation
6 Journal de Mathématiques Pures et Appliquées. Neuvième Série
6 Journal of Nonlinear Science
6 Computing and Visualization in Science
6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
5 Journal of Engineering Mathematics
5 Journal of Functional Analysis
5 Proceedings of the American Mathematical Society
5 Mathematical Problems in Engineering
5 Acta Mathematica Sinica. English Series
5 Journal of Evolution Equations
5 Archives of Computational Methods in Engineering
5 Journal of Applied Mathematics and Computing
5 Boundary Value Problems
4 Bulletin of the Australian Mathematical Society
4 International Journal of Engineering Science
4 Nonlinearity
4 Journal of Optimization Theory and Applications
4 Mathematische Annalen
4 Studies in Applied Mathematics
4 Zeitschrift für Analysis und ihre Anwendungen
4 Journal of Mathematical Sciences (New York)
4 ZAMM. 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