A finite volume scheme preserving the invariant region property for a class of semilinear parabolic equations on distorted meshes

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2023-05-26 DOI:10.1002/num.23050

Huifang Zhou, Yuanyuan Liu, Z. Sheng

引用次数: 0

Abstract

In this article, we present a finite volume scheme preserving invariant‐region‐property (IRP) for a class of semilinear parabolic equations with anisotropic diffusion coefficient on distorted meshes. The diffusion term is discretized by the finite volume scheme preserving the discrete maximum principle, and the time derivative is discretized by the backward Euler scheme. For the nonlinear system, a specially designed iteration is proposed to preserve the IRP. The IRPs are proved for both, the finite volume scheme and the nonlinear iteration. Numerical examples are presented to verify the accuracy and IRP of our scheme.

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一类半线性抛物型方程在畸变网格上的有限体积格式

本文给出了一类具有各向异性扩散系数的半线性抛物型方程在畸变网格上保持不变量区域性质(IRP)的有限体积格式。扩散项采用有限体积格式离散化，保持离散极大值原则，时间导数采用后向欧拉格式离散化。对于非线性系统，提出了一种特殊设计的迭代方法来保持IRP。证明了有限体积格式和非线性迭代的irp。数值算例验证了该方法的精度和IRP。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.