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- Gerhard Dziuk, Charles M. Elliott
- Math. Comput.
- 2013

In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces Î“ in R. The key idea is based on theâ€¦ (More)

- Charles M. Elliott, Stig LarssonAbstract
- 1995

We study a spatially semidiscrete and a completely discrete finite element model for a nonlinear system consisting of an elliptic and a parabolic partial differential equation describing the electricâ€¦ (More)

- Gerhard Dziuk, Charles M. Elliott
- Computat. and Visualiz. in Science
- 2010

In this article we define a level set method for a scalar conservation law with a diffusive flux on an evolving hypersurface Î“ (t) contained in a domain Î© âŠ‚ Rn+1. The partial differential equation isâ€¦ (More)

- Klaus Deckelnick, Charles M. Elliott, Thomas Ranner
- SIAM J. Numerical Analysis
- 2014

In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that theâ€¦ (More)

- F Bait, Charles M. Elliott, Gardiner, Spencet, Michael Six
- 1994

The viscous Cahn-Hilliard equation arises as a singular limit of the phase-field model of phase transitions. It contains both the Cahn-Hilliard and Allen-Cahn equations as particular limits. Theâ€¦ (More)

- Gerhard Dziuk, Charles M. Elliott
- SIAM J. Numerical Analysis
- 2012

In this paper we consider a time discrete evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface. In earlier papers using a suitableâ€¦ (More)

- Klaus Deckelnick, Gerhard Dziuk, Charles M. Elliott
- SIAM J. Numerical Analysis
- 2005

Abstract. We analyze a fully discrete numerical scheme for approximating the evolution of graphs for surfaces evolving by anisotropic surface diffusion. The scheme is based on the idea of secondâ€¦ (More)

- Raquel Barreira, Charles M. Elliott, Anotida Madzvamuse
- Journal of mathematical biology
- 2011

In this article we propose models and a numerical method for pattern formation on evolving curved surfaces. We formulate reaction-diffusion equations on evolving surfaces using the material transportâ€¦ (More)

- Klaus Deckelnick, Gerhard Dziuk, Charles M. Elliott
- SIAM J. Numerical Analysis
- 2003

We analyze a semidiscrete numerical scheme for approximating the evolution of axially symmetric surfaces by surface diffusion. The fourth order equation is split into two coupled second orderâ€¦ (More)