Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation
Numerical Analysis
2021-04-27 v1 Numerical Analysis
Abstract
We consider solving a generalized Allen-Cahn equation coupled with a passive convection for a given incompressible velocity field. The numerical scheme consists of the first order accurate stabilized implicit explicit time discretization and a fourth order accurate finite difference scheme, which is obtained from the finite difference formulation of the spectral element method. We prove that the discrete maximum principle holds under suitable mesh size and time step constraints. The same result also applies to construct a bound-preserving scheme for any passive convection with an incompressible velocity field.
Keywords
Cite
@article{arxiv.2104.11813,
title = {Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation},
author = {Jie Shen and Xiangxiong Zhang},
journal= {arXiv preprint arXiv:2104.11813},
year = {2021}
}