Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces
Numerical Analysis
2022-03-07 v3 Numerical Analysis
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.
Cite
@article{arxiv.2006.02274,
title = {Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces},
author = {Cedric Aaron Beschle and Balázs Kovács},
journal= {arXiv preprint arXiv:2006.02274},
year = {2022}
}