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

被引：1

作者：

Mai, Xiongfa ^{[1
]}

Zhu, Ciwen ^{[1
]}

Liu, Libin ^{[1
]}

机构：

[1] Nanning Normal Univ, Sch Math & Stat, Nanning 530100, Peoples R China

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2023年 / 18卷 / 04期

关键词：

singularly perturbed; discontinuous convection coefficient; adaptive grid algorithm; a posteriori error estimate; HYBRID DIFFERENCE SCHEME; MAXIMUM NORM; NUMERICAL-METHOD; SYSTEM; BOUNDARY;

D O I：

10.3934/nhm.2023067

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1528 / 1538

页数：11

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