SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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A numerical analysis of parabolic differential equations on evolving surfaces

D. Mansour

Abstract
A linear parabolic partial differential equation on a moving surface is discretized in space by the evolving surface finite element method. Discretization in time is done by implicit Runge-Kutta methods, aiming for higher-order accuracy in time and unconditional stability of the fully discrete scheme. Thanks to the properties of the spatial semi-discretization, the latter is established for algebraically stable and stiffly accurate Runge-Kutta methods. Under sufficient regularity conditions, optimal-order error estimates in the natural time dependent norms are shown. Numerical experiments are presented to confirm some of the theoretical results.

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