A posteriori error estimate of the weak Galerkin finite element method solving the Stokes problems on polytopal meshes

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2024-03-27 DOI:10.1002/num.23102

Shipeng Xu

引用次数: 0

Abstract

In this paper, we propose an a posteriori error estimate of the weak Galerkin finite element method (WG-FEM) solving the Stokes problems with variable coefficients. Its error estimator, based on the property of Stokes' law conservation, Helmholtz decomposition and bubble functions, yields global upper bound and local lower bound for the approximation error of the WG-FEM. Error analysis is proved to be valid under the mesh assumptions of the WG-FEM and the way can be extended to other FEMs with the property of Stokes' law conservation, for example, discontinuous Galerkin (DG) FEMs. Finally, we verify the performance of error estimator by performing a few numerical examples.

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弱 Galerkin 有限元方法解决多桌面网格上斯托克斯问题的后验误差估计

本文提出了弱伽勒金有限元法（WG-FEM）求解变系数斯托克斯问题的后验误差估计。它的误差估算器基于斯托克斯定律守恒、亥姆霍兹分解和气泡函数的特性，得出了 WG-FEM 近似误差的全局上限和局部下限。误差分析证明在 WG-FEM 的网格假设条件下是有效的，而且这种方法可以扩展到其他具有斯托克斯定律守恒特性的有限元，例如非连续加勒金（DG）有限元。最后，我们通过几个数值示例验证了误差估算器的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.