Anisotropic error analysis of weak Galerkin finite element method for singularly perturbed biharmonic problems

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2024-10-05 DOI:10.1016/j.matcom.2024.09.017

Aayushman Raina , Srinivasan Natesan , Şuayip Toprakseven

引用次数: 0

Abstract

We consider the weak Galerkin finite element approximation of the singularly perturbed biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution exhibits boundary layers near the domain boundary. Error estimates in the equivalent

H^{2} -

norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings.

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奇异扰动双谐问题弱 Galerkin 有限元方法的各向异性误差分析

我们考虑在一个具有箝位边界条件的单位方域上对奇异扰动双谐波椭圆问题进行弱 Galerkin 有限元近似。由于解在域边界附近会出现边界层，因此采用 Shishkin 网格进行域离散化。建立了等效 H2- 规范的误差估计，并证明了所提方法的均匀收敛性。给出的数值示例证实了我们的理论发现。

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

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.