English

A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation

Numerical Analysis 2023-06-02 v1 Numerical Analysis

Abstract

The paper studies a scalar auxiliary variable (SAV) method to solve the Cahn-Hilliard equation with degenerate mobility posed on a smooth closed surface {\Gamma}. The SAV formulation is combined with adaptive time stepping and a geometrically unfitted trace finite element method (TraceFEM), which embeds {\Gamma} in R3. The stability is proven to hold in an appropriate sense for both first- and second-order in time variants of the method. The performance of our SAV method is illustrated through a series of numerical experiments, which include systematic comparison with a stabilized semi-explicit method.

Keywords

Cite

@article{arxiv.2306.00318,
  title  = {A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation},
  author = {Maxim Olshanskii and Yerbol Palzhanov and Annalisa Quaini},
  journal= {arXiv preprint arXiv:2306.00318},
  year   = {2023}
}

Comments

23 pages, 12 figures