Error estimate of the finite volume scheme for the Allen–Cahn equation

被引：0
|
作者：
Pavel Strachota
Michal Beneš
机构：
[1] Czech Technical University in Prague,Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering
来源：
BIT Numerical Mathematics | 2018年 / 58卷
关键词：
Allen–Cahn equation; Error estimate; Finite volume method; Phase field; Semidiscrete scheme; Solidification; 65M08; 65M15; 80A22; 74N05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The Allen–Cahn equation originates in the phase field formulation of phase transition phenomena. It is a reaction-diffusion ODE with a nonlinear reaction term which allows the formation of a diffuse phase interface. We first introduce a model initial boundary-value problem for the isotropic variant of the equation. Its numerical solution by the method of lines is then considered, using a finite volume scheme for spatial discretization. An error estimate is derived for the solution of the resulting semidiscrete scheme. Subsequently, sample numerical simulations in two and three dimensions are presented and the experimental convergence measurement is discussed.
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页码：489 / 507
页数：18
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