Year: 2021
Author: Huifang Zhou, Zhiqiang Sheng, Guangwei Yuan
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 1 : pp. 232–260
Abstract
In this paper, we propose a new conservative gradient discretization method (GDM) for one-dimensional parabolic partial differential equations (PDEs). We use the implicit Euler method for the temporal discretization and conservative gradient discretization method for spatial discretization. The method is based on a new cell-centered meshes, and it is locally conservative. It has smaller truncation error than the classical finite volume method on uniform meshes. We use the framework of the gradient discretization method to analyze the stability and convergence. The numerical experiments show that the new method has second-order convergence. Moreover, it is more accurate than the classical finite volume method in flux error, $L^2$ error and $L^{\infty}$ error.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0047
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 1 : pp. 232–260
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Gradient discretization method mass conservation parabolic equations.
Author Details
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Analysis of the nonlinear scheme preserving the maximum principle for the anisotropic diffusion equation on distorted meshes
Sheng, Zhiqiang
Yuan, Guangwei
Science China Mathematics, Vol. 65 (2022), Iss. 11 P.2379
https://doi.org/10.1007/s11425-021-1931-3 [Citations: 4]