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arXiv · 1606.07234

High-order evolving surface finite element method for parabolic problems on evolving surfaces

Balázs Kovács
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Abstract

High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order versions of geometric approximation errors and perturbation error estimates and by the careful error analysis of a modified Ritz map. Furthermore, convergence of full discretisations using backward difference formulae and implicit Runge-Kutta methods are also shown.

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Balázs Kovács. 2016-06-23. High-order evolving surface finite element method for parabolic problems on evolving surfaces. https://arxiv.org/abs/1606.07234

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