Finite element methods for surface PDEs. Zbl 1296.65156
Dziuk, Gerhard; Elliott, Charles M. |
|
2013
|
On the Cahn-Hilliard equation with degenerate mobility. Zbl 0856.35071
Elliott, Charles M.; Garcke, Harald |
|
1996
|
On the Cahn-Hilliard equation. Zbl 0624.35048
Elliott, Charles M.; Zheng, Songmu |
|
1986
|
Computation of geometric partial differential equations and mean curvature flow. Zbl 1113.65097
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. |
|
2005
|
The global dynamics of discrete semilinear parabolic equations. Zbl 0792.65066
Elliott, C. M.; Stuart, A. M. |
|
1993
|
Weak and variational methods for moving boundary problems. Zbl 0476.35080
Elliott, C. M.; Ockendon, J. R. |
|
1982
|
Finite elements on evolving surfaces. Zbl 1120.65102
Dziuk, G.; Elliott, C. M. |
|
2007
|
A second order splitting method for the Cahn-Hilliard equation. Zbl 0668.65097
Elliott, C. M.; French, D. A.; Milner, F. A. |
|
1989
|
Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0762.65074
Copetti, M. I. M.; Elliott, C. M. |
|
1992
|
Numerical studies of the Cahn-Hilliard equation for phase separation. Zbl 0632.65113
Elliott, Charles M.; French, Donald A. |
|
1987
|
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. |
|
1996
|
The Cahn-Hilliard model for the kinetics of phase separation. Zbl 0692.73003
Elliott, C. M. |
|
1989
|
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. |
|
1991
|
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 |
|
1992
|
Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces. Zbl 0629.65118
Barrett, John W.; Elliott, Charles M. |
|
1987
|
A nonconforming finite-element method for the two-dimensional Cahn- Hilliard equation. Zbl 0686.65086
Elliott, Charles M.; French, Donald A. |
|
1989
|
Modeling and computation of two phase geometric biomembranes using surface finite elements. Zbl 1425.74323
Elliott, Charles M.; Stinner, Björn |
|
2010
|
Viscous Cahn-Hilliard equation. II: Analysis. Zbl 0855.35067
Elliott, C. M.; Stuart, A. M. |
|
1996
|
The surface finite element method for pattern formation on evolving biological surfaces. Zbl 1234.92007
Barreira, R.; Elliott, C. M.; Madzvamuse, A. |
|
2011
|
The viscous Cahn-Hilliard equation. I: Computations. Zbl 0818.35045
Bai, F.; Elliott, C. M.; Gardiner, A.; Spence, A.; Stuart, A. M. |
|
1995
|
A variational inequality approach to Hele-Shaw flow with a moving boundary. Zbl 0455.76043
Elliott, C. M.; Janovsky, V. |
|
1981
|
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. |
|
1992
|
Finite element analysis for a coupled bulk-surface partial differential equation. Zbl 1271.65138
Elliott, Charles M.; Ranner, Thomas |
|
2013
|
Finite element approximation of the Dirichlet problem using the boundary penalty method. Zbl 0614.65116
Barrett, John W.; Elliott, Charles M. |
|
1986
|
Shooting method for vortex solutions of a complex-valued Ginzburg-Landau equation. Zbl 0816.34003
Chen, Xinfu; Elliott, Charles M.; Qi, Tang |
|
1994
|
Global existence and stability of solutions to the phase field equations. Zbl 0733.35062
Elliott, C. M.; Zheng, Songmu |
|
1990
|
Evolving surface finite element method for the Cahn-Hilliard equation. Zbl 1312.65159
Elliott, Charles M.; Ranner, Thomas |
|
2015
|
Numerical computation of advection and diffusion on evolving diffuse interfaces. Zbl 1241.65081
Elliott, Charles M.; Stinner, Björn; Styles, Vanessa; Welford, Richard |
|
2011
|
Curvature dependent phase boundary motion and parabolic double obstacle problems. Zbl 0794.35092
Blowey, J. F.; Elliott, C. M. |
|
1993
|
\(L^2\)-estimates for the evolving surface finite element method. Zbl 1269.65087
Dziuk, Gerhard; Elliott, Charles M. |
|
2013
|
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 |
|
2017
|
Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. Zbl 1149.76027
Eilks, C.; Elliott, C. M. |
|
2008
|
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 |
|
2010
|
An abstract framework for parabolic PDEs on evolving spaces. Zbl 1323.35103
Alphonse, Amal; Elliott, Charles M.; Stinner, Björn |
|
2015
|
Eulerian finite element method for parabolic PDEs on implicit surfaces. Zbl 1145.65073
Dziuk, G.; Elliott, C. M. |
|
2008
|
A finite element model for the time-dependent Joule heating problem. Zbl 0846.65047
Elliott, Charles M.; Larsson, Stig |
|
1995
|
Computation of two-phase biomembranes with phase dependent material parameters using surface finite elements. Zbl 1373.74089
Elliott, Charles M.; Stinner, Björn |
|
2013
|
Error analysis of the enthalpy method for the Stefan problem. Zbl 0638.65088
Elliott, C. M. |
|
1987
|
Existence results for diffusive surface motion laws. Zbl 0876.35050
Elliott, Charles M.; Garcke, Harald |
|
1997
|
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. |
|
1996
|
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. |
|
1986
|
A surface phase field model for two-phase biological membranes. Zbl 1209.92003
Elliott, Charles M.; Stinner, Björn |
|
2010
|
Asymptotics for a parabolic double obstacle problem. Zbl 0814.35044
Chen, Xinfu; Elliott, Charles M. |
|
1994
|
An ALE ESFEM for solving PDEs on evolving surfaces. Zbl 1259.65147
Elliott, Charles M.; Styles, Vanessa |
|
2012
|
Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equation. Zbl 0888.35047
Elliott, C. M.; Kostin, I. N. |
|
1996
|
Unfitted finite element methods using bulk meshes for surface partial differential equations. Zbl 1307.65164
Deckelnick, Klaus; Elliott, Charles M.; Ranner, Thomas |
|
2014
|
A fully discrete evolving surface finite element method. Zbl 1267.65128
Dziuk, Gerhard; Elliott, Charles M. |
|
2012
|
An Eulerian approach to transport and diffusion on evolving implicit surfaces. Zbl 1220.65132
Dziuk, G.; Elliott, C. M. |
|
2010
|
Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model. Zbl 0905.35084
Chen, Zhiming; Elliott, C. M.; Qi, Tang |
|
1998
|
A dynamic contact problem in thermoelasticity. Zbl 0818.73061
Elliott, C. M.; Qi, Tang |
|
1994
|
A one-dimensional quasi-static contact problem in linear thermoelasticity. Zbl 0779.73051
Copetti, M. I. M.; Elliott, C. M. |
|
1993
|
Convergence of numerical solutions to the Allen-Cahn equation. Zbl 0992.65096
Chen, Xinfu; Elliott, Charlie M.; Gardiner, Andy; Zhao, Jennifer Jing |
|
1998
|
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. |
|
1984
|
Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Zbl 1081.35115
Deckelnick, Klaus; Elliott, Charles M. |
|
2004
|
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. |
|
1981
|
The limit of the anisotropic double-obstacle Allen-Cahn equation. Zbl 0865.35073
Elliott, Charles M.; Schätzle, Reiner |
|
1996
|
On some linear parabolic PDEs on moving hypersurfaces. Zbl 1333.35306
Alphonse, Amal; Elliott, Charles M.; Stinner, Björn |
|
2015
|
Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface. Zbl 1200.35018
Elliott, Charles M.; Stinner, Björn |
|
2009
|
A free-boundary model for diffusion-induced grain boundary motion. Zbl 0986.35136
Fife, P. C.; Cahn, J. W.; Elliott, C. M. |
|
2001
|
Total flux estimates for a finite-element approximation of elliptic equations. Zbl 0619.65098
Barrett, John W.; Elliott, Charles M. |
|
1987
|
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087
Elliott, Charles M.; Garcke, Harald |
|
1997
|
A phase-field model with a double obstacle potential. Zbl 0809.35168
Blowey, J. F.; Elliott, C. M. |
|
1994
|
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225
Elliott, Charles M.; Garcke, Harald |
|
1997
|
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. |
|
1980
|
Percolation in gently sloping beaches. Zbl 0536.76085
Aitchison, J. M.; Elliott, C. M.; Ockendon, J. R. |
|
1983
|
Numerical diffusion-induced grain boundary motion. Zbl 0991.35095
Deckelnick, K.; Elliott, C. M.; Styles, V. |
|
2001
|
Fully discrete finite element approximation for anisotropic surface diffusion of graphs. Zbl 1094.65098
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. |
|
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. |
|
2007
|
A finite-element analysis of critical-state models for type-II superconductivity in 3D. Zbl 1119.82046
Elliott, Charles M.; Kashima, Yohei |
|
2007
|
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 |
|
2017
|
Error analysis for an ALE evolving surface finite element method. Zbl 1318.65063
Elliott, Charles M.; Venkataraman, Chandrasekhar |
|
2015
|
Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces. Zbl 1058.65097
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. |
|
2003
|
Zeros of a complex Ginzburg-Landau order parameter with applications to superconductivity. Zbl 0817.35112
Elliott, C. M.; Matano, H.; Qi, Tang |
|
1994
|
Approximation of curvature dependent interface motion. Zbl 0881.65131
Elliott, C. M. |
|
1997
|
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. |
|
1985
|
Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Zbl 1368.74039
Elliott, Charles M.; Fritz, Hans; Hobbs, Graham |
|
2017
|
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. |
|
2009
|
A variational approach to particles in lipid membranes. Zbl 1362.35311
Elliott, Charles M.; Gräser, Carsten; Hobbs, Graham; Kornhuber, Ralf; Wolf, Maren-Wanda |
|
2016
|
The free boundary of a flow in a porous body heated from its boundary. Zbl 0621.76101
DiBenedetto, Emmanuele; Elliott, Charles M.; Friedman, Avner |
|
1986
|
Losing a graph with surface diffusion. Zbl 0993.35042
Elliott, Charles M.; Maier-Paape, Stanislaus |
|
2001
|
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 |
|
2018
|
A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains. Zbl 07528292
Elliott, C. M.; Ranner, T. |
|
2021
|
The limit of the fully anisotropic double-obstacle Allen-Cahn equation in the nonsmooth case. Zbl 0870.35128
Elliott, Charles M.; Schätzle, Reiner |
|
1997
|
A practical finite element approximation of a semi-definite Neumann problem on a curved domain. Zbl 0617.65110
Barrett, John W.; Elliott, Charles M. |
|
1987
|
On the convergence of a one-step method for the numerical solution of an ordinary differential inclusion. Zbl 0598.65052
Elliott, C. M. |
|
1985
|
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. |
|
1988
|
Dynamic boundary conditions for Hamilton–Jacobi equations. Zbl 1030.35115
Elliott, C. M.; Giga, Y.; Goto, S. |
|
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. |
|
1997
|
Optimal control of elliptic PDEs at points. Zbl 1433.49041
Brett, Charles; Dedner, Andreas; Elliott, Charles |
|
2016
|
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. |
|
1998
|
Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean-curvature flow. Zbl 0873.35039
Elliott, Charles M.; Paolini, Maurizio; Schätzle, Reiner |
|
1996
|
Finite element error bounds for a curve shrinking with prescribed normal contact to a fixed boundary. Zbl 0921.65009
Deckelnick, Klaus; Elliott, Charles M. |
|
1998
|
Well-posedness of a fractional porous medium equation on an evolving surface. Zbl 1334.35365
Alphonse, Amal; Elliott, Charles M. |
|
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 |
|
2016
|
Numerical analysis of an inverse problem for the eikonal equation. Zbl 1244.65093
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa |
|
2011
|
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 |
|
2015
|
A Stefan problem on an evolving surface. Zbl 1353.35317
Alphonse, Amal; Elliott, Charles M. |
|
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 |
|
2015
|
Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. Zbl 07565226
Elliott, Charles M.; Garcke, Harald; Kovács, Balázs |
|
2022
|
Computations of bidirectional grain boundary dynamics in thin metallic films. Zbl 1020.82006
Elliott, C. M.; Styles, V. |
|
2003
|
Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs. Zbl 1509.35391
Alphonse, Amal; Caetano, Diogo; Djurdjevac, Ana; Elliott, Charles M. |
|
2023
|
Regularization and separation for evolving surface Cahn-Hilliard equations. Zbl 1531.35328
Caetano, Diogo; Elliott, Charles M.; Grasselli, Maurizio; Poiatti, Andrea |
|
2023
|
Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. Zbl 07565226
Elliott, Charles M.; Garcke, Harald; Kovács, Balázs |
|
2022
|
On the sharp interface limit of a phase field model for near spherical two phase biomembranes. Zbl 1489.35287
Elliott, Charles M.; Hatcher, Luke; Stinner, Björn |
|
2022
|
A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains. Zbl 07528292
Elliott, C. M.; Ranner, T. |
|
2021
|
Cahn-Hilliard equations on an evolving surface. Zbl 1479.35902
Caetano, D.; Elliott, C. M. |
|
2021
|
Domain formation via phase separation for spherical biomembranes with small deformations. Zbl 1479.35013
Elliott, C. M.; Hatcher, L. |
|
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. |
|
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. |
|
2020
|
Second order splitting of a class of fourth order PDEs with point constraints. Zbl 1446.65167
Elliott, Charles M.; Herbert, Philip J. |
|
2020
|
Second order splitting for a class of fourth order equations. Zbl 1426.65175
Elliott, Charles M.; Fritz, Hans; Hobbs, Graham |
|
2019
|
Binary recovery via phase field regularization for first-arrival traveltime tomography. Zbl 1431.65153
Dunbar, Oliver R. A.; Elliott, Charles M. |
|
2019
|
Hamilton-Jacobi equations on an evolving surface. Zbl 1426.65134
Deckelnick, Klaus; Elliott, Charles M.; Miura, Tatsu-Hiko; Styles, Vanessa |
|
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 |
|
2018
|
Evolving surface finite element methods for random advection-diffusion equations. Zbl 1407.65258
Djurdjevac, Ana; Elliott, Charles M.; Kornhuber, Ralf; Ranner, Thomas |
|
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 |
|
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 |
|
2017
|
Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Zbl 1368.74039
Elliott, Charles M.; Fritz, Hans; Hobbs, Graham |
|
2017
|
Emerging developments in interfaces and free boundaries. Abstracts from the workshop held January 22–28, 2017. Zbl 1390.00086
|
|
2017
|
A variational approach to particles in lipid membranes. Zbl 1362.35311
Elliott, Charles M.; Gräser, Carsten; Hobbs, Graham; Kornhuber, Ralf; Wolf, Maren-Wanda |
|
2016
|
Optimal control of elliptic PDEs at points. Zbl 1433.49041
Brett, Charles; Dedner, Andreas; Elliott, Charles |
|
2016
|
Well-posedness of a fractional porous medium equation on an evolving surface. Zbl 1334.35365
Alphonse, Amal; Elliott, Charles M. |
|
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 |
|
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 |
|
2016
|
Evolving surface finite element method for the Cahn-Hilliard equation. Zbl 1312.65159
Elliott, Charles M.; Ranner, Thomas |
|
2015
|
An abstract framework for parabolic PDEs on evolving spaces. Zbl 1323.35103
Alphonse, Amal; Elliott, Charles M.; Stinner, Björn |
|
2015
|
On some linear parabolic PDEs on moving hypersurfaces. Zbl 1333.35306
Alphonse, Amal; Elliott, Charles M.; Stinner, Björn |
|
2015
|
Error analysis for an ALE evolving surface finite element method. Zbl 1318.65063
Elliott, Charles M.; Venkataraman, Chandrasekhar |
|
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 |
|
2015
|
A Stefan problem on an evolving surface. Zbl 1353.35317
Alphonse, Amal; Elliott, Charles M. |
|
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 |
|
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. |
|
2015
|
Time-periodic solutions of advection-diffusion equations on moving hypersurfaces. Zbl 1320.35021
Elliott, Charles M.; Fritz, Hans |
|
2015
|
Unfitted finite element methods using bulk meshes for surface partial differential equations. Zbl 1307.65164
Deckelnick, Klaus; Elliott, Charles M.; Ranner, Thomas |
|
2014
|
Phase field methods for binary recovery. Zbl 1320.49024
Brett, Charles; Elliott, Charles M.; Dedner, Andreas S. |
|
2014
|
Finite element methods for surface PDEs. Zbl 1296.65156
Dziuk, Gerhard; Elliott, Charles M. |
|
2013
|
Finite element analysis for a coupled bulk-surface partial differential equation. Zbl 1271.65138
Elliott, Charles M.; Ranner, Thomas |
|
2013
|
\(L^2\)-estimates for the evolving surface finite element method. Zbl 1269.65087
Dziuk, Gerhard; Elliott, Charles M. |
|
2013
|
Computation of two-phase biomembranes with phase dependent material parameters using surface finite elements. Zbl 1373.74089
Elliott, Charles M.; Stinner, Björn |
|
2013
|
Interfaces and free boundaries: analysis, control and simulation. Abstracts from the workshop held March 24–30, 2013. Zbl 1349.00157
|
|
2013
|
An ALE ESFEM for solving PDEs on evolving surfaces. Zbl 1259.65147
Elliott, Charles M.; Styles, Vanessa |
|
2012
|
A fully discrete evolving surface finite element method. Zbl 1267.65128
Dziuk, Gerhard; Elliott, Charles M. |
|
2012
|
The surface finite element method for pattern formation on evolving biological surfaces. Zbl 1234.92007
Barreira, R.; Elliott, C. M.; Madzvamuse, A. |
|
2011
|
Numerical computation of advection and diffusion on evolving diffuse interfaces. Zbl 1241.65081
Elliott, Charles M.; Stinner, Björn; Styles, Vanessa; Welford, Richard |
|
2011
|
Numerical analysis of an inverse problem for the eikonal equation. Zbl 1244.65093
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa |
|
2011
|
Geometric partial differential equations: theory, numerics and applications. Abstracts from the workshop held November 27 – December 3, 2011. Zbl 1349.00149
|
|
2011
|
Modeling and computation of two phase geometric biomembranes using surface finite elements. Zbl 1425.74323
Elliott, Charles M.; Stinner, Björn |
|
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 |
|
2010
|
A surface phase field model for two-phase biological membranes. Zbl 1209.92003
Elliott, Charles M.; Stinner, Björn |
|
2010
|
An Eulerian approach to transport and diffusion on evolving implicit surfaces. Zbl 1220.65132
Dziuk, G.; Elliott, C. M. |
|
2010
|
Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface. Zbl 1200.35018
Elliott, Charles M.; Stinner, Björn |
|
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. |
|
2009
|
Optimal control of the propagation of a graph in inhomogeneous media. Zbl 1282.49003
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa |
|
2009
|
Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. Zbl 1149.76027
Eilks, C.; Elliott, C. M. |
|
2008
|
Eulerian finite element method for parabolic PDEs on implicit surfaces. Zbl 1145.65073
Dziuk, G.; Elliott, C. M. |
|
2008
|
Finite elements on evolving surfaces. Zbl 1120.65102
Dziuk, G.; Elliott, C. M. |
|
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. |
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2007
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A finite-element analysis of critical-state models for type-II superconductivity in 3D. Zbl 1119.82046
Elliott, Charles M.; Kashima, Yohei |
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2007
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Propagation of graphs in two-dimensional inhomogeneous media. Zbl 1126.65073
Deckelnick, Klaus; Elliott, Charles M. |
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2006
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On macroscopic critical state models of superconductivity in 3D. Zbl 1143.65379
Elliott, Charles M.; Kashima, Yohei |
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2006
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Computation of geometric partial differential equations and mean curvature flow. Zbl 1113.65097
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. |
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2005
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Fully discrete finite element approximation for anisotropic surface diffusion of graphs. Zbl 1094.65098
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. |
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2005
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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. |
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2005
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Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Zbl 1081.35115
Deckelnick, Klaus; Elliott, Charles M. |
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2004
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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. |
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2004
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Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces. Zbl 1058.65097
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M. |
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2003
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Dynamic boundary conditions for Hamilton–Jacobi equations. Zbl 1030.35115
Elliott, C. M.; Giga, Y.; Goto, S. |
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2003
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Computations of bidirectional grain boundary dynamics in thin metallic films. Zbl 1020.82006
Elliott, C. M.; Styles, V. |
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2003
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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. |
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2002
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A free-boundary model for diffusion-induced grain boundary motion. Zbl 0986.35136
Fife, P. C.; Cahn, J. W.; Elliott, C. M. |
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2001
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Numerical diffusion-induced grain boundary motion. Zbl 0991.35095
Deckelnick, K.; Elliott, C. M.; Styles, V. |
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2001
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Losing a graph with surface diffusion. Zbl 0993.35042
Elliott, Charles M.; Maier-Paape, Stanislaus |
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2001
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An existence and uniqueness result for a phase-filed model of diffusion-induced grain-boundary motion. Zbl 0989.35006
Deckelnick, Klaus; Elliott, Charles M. |
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2001
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Numerical analysis of a mean field model of superconducting vortices. Zbl 0984.82042
Elliott, Charles M.; Styles, Vanessa |
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2001
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Local and global existence results for anisotropic Hele-Shaw flows. Zbl 0922.76150
Deckelnick, Klaus; Elliott, Charles M. |
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1999
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Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model. Zbl 0905.35084
Chen, Zhiming; Elliott, C. M.; Qi, Tang |
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1998
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Convergence of numerical solutions to the Allen-Cahn equation. Zbl 0992.65096
Chen, Xinfu; Elliott, Charlie M.; Gardiner, Andy; Zhao, Jennifer Jing |
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1998
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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. |
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1998
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Finite element error bounds for a curve shrinking with prescribed normal contact to a fixed boundary. Zbl 0921.65009
Deckelnick, Klaus; Elliott, Charles M. |
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1998
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Crystalline curvature flow of a graph in a variational setting. Zbl 0959.35168
Elliott, Charles M.; Gardiner, Andrew R.; Schätzle, Reiner |
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1998
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Existence results for diffusive surface motion laws. Zbl 0876.35050
Elliott, Charles M.; Garcke, Harald |
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1997
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Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087
Elliott, Charles M.; Garcke, Harald |
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1997
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Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225
Elliott, Charles M.; Garcke, Harald |
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1997
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Approximation of curvature dependent interface motion. Zbl 0881.65131
Elliott, C. M. |
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1997
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The limit of the fully anisotropic double-obstacle Allen-Cahn equation in the nonsmooth case. Zbl 0870.35128
Elliott, Charles M.; Schätzle, Reiner |
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1997
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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. |
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1997
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Vortices, dislocations and line singularities in partial differential equations. Zbl 0886.00011
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1997
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On the Cahn-Hilliard equation with degenerate mobility. Zbl 0856.35071
Elliott, Charles M.; Garcke, Harald |
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1996
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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. |
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1996
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Viscous Cahn-Hilliard equation. II: Analysis. Zbl 0855.35067
Elliott, C. M.; Stuart, A. M. |
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1996
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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. |
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1996
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Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equation. Zbl 0888.35047
Elliott, C. M.; Kostin, I. N. |
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1996
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The limit of the anisotropic double-obstacle Allen-Cahn equation. Zbl 0865.35073
Elliott, Charles M.; Schätzle, Reiner |
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1996
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Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean-curvature flow. Zbl 0873.35039
Elliott, Charles M.; Paolini, Maurizio; Schätzle, Reiner |
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1996
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The viscous Cahn-Hilliard equation. I: Computations. Zbl 0818.35045
Bai, F.; Elliott, C. M.; Gardiner, A.; Spence, A.; Stuart, A. M. |
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1995
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A finite element model for the time-dependent Joule heating problem. Zbl 0846.65047
Elliott, Charles M.; Larsson, Stig |
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1995
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Shooting method for vortex solutions of a complex-valued Ginzburg-Landau equation. Zbl 0816.34003
Chen, Xinfu; Elliott, Charles M.; Qi, Tang |
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1994
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Asymptotics for a parabolic double obstacle problem. Zbl 0814.35044
Chen, Xinfu; Elliott, Charles M. |
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1994
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A dynamic contact problem in thermoelasticity. Zbl 0818.73061
Elliott, C. M.; Qi, Tang |
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1994
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A phase-field model with a double obstacle potential. Zbl 0809.35168
Blowey, J. F.; Elliott, C. M. |
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1994
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...and 44 more Documents |