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arXiv · 2006.02274

Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces

Cedric Aaron Beschle·Balázs Kovács
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Abstract

In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix-vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.

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Cedric Aaron Beschle, Balázs Kovács. 2020-06-03. Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces. https://arxiv.org/abs/2006.02274

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