Location:	Mantell Building
Email:	C.M.Elliott@sussex.ac.uk

Biography

Charlie Elliott's personal webpages

Research

 
Numerical Analysis, Partial Differential Equations, Free Boundary Problems, Phase Transitions.

My research is mainly concerned with the modelling, analysis and computation of problems in the physical sciences leading to partial differential equations.

My interests range from rigorous analysis of equations and numerical methods to models and scientific computation. I collaborate with mathematicians throughout the world. The applied mathematics group at Sussex has taken part in a number of European Union funded programmes.

Possible topics for graduate student research programmes include:

• Geometric evolution problem with many applications in materials science.

• Partial differential equations on surfaces

• Phase separation in alloys and fluids coupling Cahn-Hilliard equations to equations of solid and fluid mechanics

• Mathematical modelling of bio-membranes

• Computations and analysis in mathematical superconductivity

• Optimal control of interfaces and free boundaries

• Finite element approximation of nonlinear partial differential equations

• Finite volume/finite element methods for first order Hamilton-Jacobi equations

  Selected publications

  2007

  Finite elements on evolving surfaces (with Dziuk, G) in IMAJ Numerical Analysis Volume 27 pp. 262--292

  2005

  Computation of Geometric PDEs and Mean Curvature Flow (with Deckelnick, K P and Dziuk, G) in Acts Numerica Volume CUP 14 pp. 139-232

  Fully discrete semi-implicit second order splitting for anisotropic surface diffusion of graphs (with Deckelnick, K P and Dziuk, G) in SIAM J. Num. Anal. Volume 43 pp. 1112-1138

  2004

  Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities (with Deckelnick, K P) in Interfaces and Free Boundaries Volume 6 pp. 329-349

  2003

  Dynamic Boundary cndition for Hamilton-Jacobi equations (with Giga, Y and Goto, S) in SIAM J. Math. Anal. Volume 34 pp. 861-881

  Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces (with Deckelnick, P K and Dziuk, G) in SIAM J. Num. Anal. Volume 41 pp. 2161-2179

  1998

  Viscosity solutions of a degenerate parabolic elliptic system arising in the mean field theory of superconductivity (with Sch¿tzle R and Stoth B) Archive for Rational Mechanics and Analysis: Archive for Rational Mechanics and Analysis Volume 145 pp. 99-127 ISBN 0003-9527

  1997

  The limit of the fully anisotropic double obstacle Allen-Cahn equation in the non-smooth case (with Sch¿tzle R) SIAM Journal of Mathematical Analysis: SIAM Journal of Mathematical Analysis Volume 28 pp. 274-303 ISBN 1095-7154