A New Upwind Finite Volume Element Method for Convection-Diffusion-Reaction Problems on Quadrilateral Meshes

被引：0

作者：

Li, Ang ^{[1
]}

Yang, Hongtao ^{[1
]}

Gao, Yulong ^{[2
]}

Li, Yonghai ^{[1
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

[2] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2024年 / 35卷 / 01期

基金：

中国国家自然科学基金;

关键词：

upwind finite volume method; coercivity; optimal convergence rate in L2 norm; Convection-diffusion-reaction; COMPLETE FLUX SCHEME; PARABOLIC PROBLEMS; EULER EQUATIONS; PRINCIPLE; ACCURACY; GRIDS;

D O I：

10.4208/cicp.OA-2023-0189

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper is devoted to constructing and analyzing a new upwind finite volume element method for anisotropic convection-diffusion-reaction problems on general quadrilateral meshes. We prove the coercivity, and establish the optimal error estimates in H1 and L2 norm respectively. The novelty is the discretization of convection term, which takes the two terms Taylor expansion. This scheme has not only optimal first-order accuracy in H1 norm, but also optimal second-order accuracy in L2 norm, both for dominant diffusion and dominant convection. Numerical experiments confirm the theoretical results.

引用

页码：239 / 272

页数：34

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