Evolving surface finite element method for the Cahn-Hilliard equation
Numerical Analysis
2014-05-28 v3 Analysis of PDEs
Abstract
We use the evolving surface finite element method to solve a Cahn- Hilliard equation on an evolving surface with prescribed velocity. We start by deriving the equation using a conservation law and appropriate transport for- mulae and provide the necessary functional analytic setting. The finite element method relies on evolving an initial triangulation by moving the nodes accord- ing to the prescribed velocity. We go on to show a rigorous well-posedness result for the continuous equations by showing convergence, along a subse- quence, of the finite element scheme. We conclude the paper by deriving error estimates and present various numerical examples.
Cite
@article{arxiv.1310.4068,
title = {Evolving surface finite element method for the Cahn-Hilliard equation},
author = {Charles M. Elliott and Thomas Ranner},
journal= {arXiv preprint arXiv:1310.4068},
year = {2014}
}