𝐿²-estimates for the evolving surface finite element method

Dziuk, Gerhard; Elliott, Charles

doi:10.1090/S0025-5718-2012-02601-9

$L^2$-estimates for the evolving surface finite element method
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by Gerhard Dziuk and Charles M. Elliott;

Math. Comp. 82 (2013), 1-24

DOI: https://doi.org/10.1090/S0025-5718-2012-02601-9

Published electronically: April 13, 2012

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Abstract:

In this paper we consider the evolving surface finite element meth- od for the advection and diffusion of a conserved scalar quantity on a moving surface. In an earlier paper using a suitable variational formulation in time dependent Sobolev space we proposed and analysed a finite element method using surface finite elements on evolving triangulated surfaces. An optimal order $H^1$-error bound was proved for linear finite elements. In this work we prove the optimal error bound in $L^2(\Gamma (t))$ uniformly in time.

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