用于四边形网格上对流-扩散-反作用问题的新型上风有限体积元素法

IF 2.6 3区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Computational Physics Pub Date : 2024-01-01 DOI:10.4208/cicp.oa-2023-0189

Ang Li,Hongtao Yang,Yulong Gao, Yonghai Li

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引用次数: 0

摘要

本文致力于构建和分析一种新的上风有限体积元方法，该方法适用于一般四边形网格上的各向异性对流-扩散-反应问题。我们证明了该方法的矫顽力，并分别在 $H^1$ 和 $L^2$ 规范下建立了最优误差估计。新颖之处在于对流项的离散化，它采用了两期泰勒展开。该方案不仅在 $H^1$ 准则下具有最优的一阶精度，而且在 $L^2$ 准则下具有最优的二阶精度，同时适用于显性扩散和显性对流。数值实验证实了理论结果。

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

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 $H^1$ and $L^2$ 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 $H^1$ norm, but also optimal second-order accuracy in $L^2$ norm, both for dominant diffusion and dominant convection. Numerical experiments confirm the theoretical results.

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来源期刊

Communications in Computational Physics 物理-物理：数学物理

CiteScore

4.70

自引率

5.40%

发文量

审稿时长

9 months

期刊介绍： Communications in Computational Physics (CiCP) publishes original research and survey papers of high scientific value in computational modeling of physical problems. Results in multi-physics and multi-scale innovative computational methods and modeling in all physical sciences will be featured.