Article

Deckelnick, Klaus, Elliott, Charles M, Miura, Tatsu-Hiko and Styles, Vanessa (2019) Hamilton-Jacobi equations on an evolving surface. Mathematics of Computation. ISSN 0025-5718

Elliott, Charles M, Ranner, Thomas and Venkataraman, Chandrasekhar (2017) Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. SIAM Journal on Mathematical Analysis, 49 (1). pp. 360-397. ISSN 0036-1410

Deckelnick, Klaus, Elliott, Charles M and Styles, Vanessa (2016) Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient. Inverse Problems, 32 (4). a045008. ISSN 0266-5611

Venkataraman, Chandrasekhar and Elliott, Charles M (2015) Error analysis for an ALE evolving surface finite element method. Numerical Methods for Partial Differential Equations, 31 (2). pp. 459-499. ISSN 0749-159X

Duncan, A M, Elliott, C M, Pavliotis, G A and Stuart, A M (2015) A multiscale analysis of diffusions on rapidly varying surfaces. Journal of Nonlinear Science, 25 (2). pp. 389-449. ISSN 0938-8974

Elliott, Charles Martin and Styles, Vanessa (2012) An ALE ESFEM for solving PDEs on evolving surfaces. Milan Journal of Mathematics, 80 (2). pp. 469-501. ISSN 1424-9286

Elliott, Charles M, Stinner, Björn and Venkataraman, Chandrasekhar (2012) Modelling cell motility and chemotaxis with evolving surface finite elements. Journal of the Royal Society, Interface, 9 (76). pp. 3027-3044. ISSN 1742-5662

Elliott, Charles M, Stinner, Björn, Styles, Vanessa and Welford, Richard (2011) Numerical computation of advection and diffusion on evolving diffuse interfaces. IMA Journal of Numerical Analysis, 31. pp. 786-812. ISSN 0272-4979

Styles, Vanessa, Elliott, Charles and Deckelnick, Klaus (2011) Numerical analysis of an inverse problem for the eikonal equation. Numerische Mathematik, 119 (2). pp. 245-269. ISSN 0029-599X

Deckelnick, Klaus, Elliott, Charles M and Styles, Vanessa (2009) Optimal Control of the Propagation of a Graph in Inhomogeneous Media. SIAM Journal on Control and Optimization, 48 (3). pp. 1335-1352. ISSN 0363-0129

Dziuk, G and Elliott, C M (2007) Finite elements on evolving surfaces. IMA Journal of Numerical Analysis, 27. p. 262. ISSN 0272-4979

Elliott, Charles Martin, Gawron, B, Maier-Paape, S and Van Vleck, ES (2006) Discrete dynamics for convex and non-convex smoothing functionals in PDE based image restoration. Communications on Pure and Applied Analysis, 5 (1). pp. 181-200. ISSN 1534-0392

Deckelnick, K and Elliott, Charles Martin (2006) Propagation of graphs in two-dimensional inhomogeneous media. Applied Numerical Mathematics, 56 (9). ISSN 0168-9274

Deckelnick, Klaus, Dziuk, Gerhard and Elliott, Charles M (2005) Computation of Geometric PDEs and Mean Curvature Flow. Acts Numerica, CUP 14. pp. 139-232.

Elliott, C M, Kay, D and Styles, V (2005) Finite element analysis of a current density-electric field formulation of Bean's model for superconductivity. IMA Journal of Numerical Analysis, 25 (1). pp. 182-204. ISSN 0272-4979

Elliott, C M, Kay, D and Styles, V (2005) Finite element analysis of a current density-electric field formulation of Bean's model for superconductivity. IMA Journal of Numerical Analysis, 25. pp. 182-204. ISSN 0272-4979

Deckelnick, Klaus, Dziuk, Gerhard and Elliott, Charles M (2005) Fully discrete semi-implicit second order splitting for anisotropic surface diffusion of graphs. SIAM Journal on Numerical Analysis, 43 (3). pp. 1112-1138. ISSN 0036-1429

Deckelnick, G, Elliott, Charles Martin and Dziuk, K (2005) Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, 14. pp. 139-232. ISSN 0962-4929

Deckelnick, Klaus and Elliott, Charles M (2004) Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Interfaces and Free Boundaries, 6 (3). pp. 329-349. ISSN 1463-9963

Elliott, C M, Kay, D and Styles, V (2004) A finite element approximation of a variational inequality formulation of Bean's model for superconductivity. SIAM Journal on Numerical Analysis, 42 (3). pp. 1324-1341. ISSN 0036-1429

Styles, V and Elliott, C M (2003) Computations of bidirectional grain boundary dynamics in thin metallic films. Journal of Computational Physics, 187 (2). pp. 524-543. ISSN 0021-9991

Elliott, C M, Giga, Y and Goto, S (2003) Dynamic Boundary cndition for Hamilton-Jacobi equations. SIAM Journal on Mathematical Analysis, 34 (4). pp. 861-881. ISSN 0036-1410

Elliott, Charles Martin, Goto, S and Giga, Y (2003) Dynamic boundary conditions for Hamilton-Jacobi equations. SIAM Journal on Mathematical Analysis, 34 (4). pp. 861-881. ISSN 0036-1410

Deckelnick, K, Dziuk, G and Elliott, Charles Martin (2003) Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces. SIAM Journal on Numerical Analysis, 41 (6). pp. 2161-2179. ISSN 0036-1429

Deckelnick, K, Elliott, Charles Martin and Styles, Vanessa (2002) Analysis and computations for a model of quasi-static deformation of a thinning sheet arising in superplastic forming. European Journal of Applied Mathematics, 13 (04). pp. 403-429. ISSN 0956-7925

Briggs, AJ, Claissel, JR and Elliott, Charles Martin (2002) Finite-difference approximation of a one-dimensional Hamilton-Jacobi/elliptic system arising in superconductivity. IMA Journal of Numerical Analysis, 22 (1). pp. 89-131. ISSN 0272-4979

Elliott, Charles M and Styles, Vanessa (2001) Numerical analysis of a mean field model of superconducting vortices. IMA Journal of Numerical Analysis, 21 (1). pp. 1-51. ISSN 0272-4979

Deckelnick, Klaus, Elliott, Charlie and Styles, Vanessa (2001) Numerical diffusion induced grain boundary motion. Interfaces and Free Boundary, 3 (4). pp. 393-414. ISSN 1463-9963

Elliott, Charles M and Styles, Vanessa (2000) Flux pinning and boundary nucleation of vorticity in a mean field model of superconducting vortices. Interfaces and Free Boundaries, 2. pp. 143-180. ISSN 1463-9963

Deckelnick, Klaus and Elliott, Charles M (1999) Local and global existence results for anisotropic Hele-Shaw flows. Proceedings of the Royal Society of Edinburgh Section A, 129 (2). pp. 265-294. ISSN 0308-2105

Elliott, Charles M, Schätzle, Reiner and Stoth, Barbara E E (1998) Viscosity solutions of a degenerate parabolic-elliptic system arising in the mean-field theory of superconductivity. Archive for Rational Mechanics and Analysis, 145 (2). pp. 99-127. ISSN 0003-9527

Deckelnick, K and Elliott, C M (1998) Finite element error bounds for curve shrinking with prescribed normal contact to a fixed boundary. IMA Journal of Numerical Analysis, 18. pp. 635-654. ISSN 0272-4979

Chen, Zhiming, Elliott, C M and Qi, Tang (1998) Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model. Mathematical Modelling and Numerical Analysis, 32 (1). pp. 25-50. ISSN 0764583X

Elliott, Charles M and Schätzle, Reiner (1997) The limit of the fully anisotropic double obstacle Allen-Cahn equation in the non-smooth case. SIAM Journal of Mathematical Analysis, 28. pp. 274-303. ISSN 1095-7154

Elliott, Charles M and Garcke, Harald (1997) Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Physica D: Nonlinear Phenomena, 109 (3-4). pp. 242-256. ISSN 0167-2789

Conference or Workshop Item

Elliott, C M and Styles, V M (1999) Numerical approximation of vortex density evolution in a superconductor. In: 18th Dundee Biennial Conference on Numerical Analysis, UNIV DUNDEE, DUNDEE, SCOTLAND, JUN 29-JUL 02, 1999.

Conference Proceedings

Elliott, Charles Martin, Stinner, Bjorn, Styles, Vanessa, Venkataraman, Chandrasekhar and Unset (2015) Modelling and simulation of cell migration in heterogeneous media. 4th International Conference Computational & Mathematical Biomedical Engineering, Paris, France, 29 June - 01 July, 2015. Published in: Nithiarasu, Perumal and Budyn, Elisa, (eds.) CMBE15: 4th International Conference on Computational & Mathematical Biomedical Engineering, 29th June - 1st July 2015 École Normale Supéerieure de Cachan, Cachan (Paris) France. 401-404. CMBE, Swansea, UK. ISBN 9780956291431