具有不连续对流系数的奇摄动对流扩散方程的自适应网格法

IF 1.2 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Networks and Heterogeneous Media Pub Date : 2023-01-01 DOI:10.3934/nhm.2023067

Xiong-fa Mai, Ciwen Zhu, Libin Liu

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引用次数: 0

摘要

本文提出了一种自适应网格法，用于求解具有不连续对流系数的奇摄动对流扩散问题。首先，在除固定跳点外的任意非均匀网格上，采用迎风有限差分格式对该问题进行离散化。然后，导出一阶最大范数的后验误差估计。在此基础上，基于后验误差估计和网格均匀分布原理，构造了自适应网格生成算法。最后，给出了一些数值实验来支持我们的理论估计。

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An adaptive grid method for a singularly perturbed convection-diffusion equation with a discontinuous convection coefficient

In this paper, an adaptive grid method is put forward to solve a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient. First, this problem is discretized by using an upwind finite difference scheme on an arbitrary nonuniform grid except the fixed jump point. Then, a first-order maximum norm a posterior error estimate is derived. Further, based on this a posteriori error estimation and the mesh equidistribution principle, an adaptive grid generation algorithm is constructed. Finally, some numerical experiments are presented that support our theoretical estimate.

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来源期刊

Networks and Heterogeneous Media 数学-数学跨学科应用

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： NHM offers a strong combination of three features: Interdisciplinary character, specific focus, and deep mathematical content. Also, the journal aims to create a link between the discrete and the continuous communities, which distinguishes it from other journals with strong PDE orientation. NHM publishes original contributions of high quality in networks, heterogeneous media and related fields. NHM is thus devoted to research work on complex media arising in mathematical, physical, engineering, socio-economical and bio-medical problems.