A Conservative Gradient Discretization Method for Parabolic Equations

A Conservative Gradient Discretization Method for Parabolic Equations

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

Huifang Zhou

Zhiqiang Sheng

Guangwei Yuan

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    https://doi.org/10.1007/s11425-021-1931-3 [Citations: 4]