弱 Galerkin 有限元方法对奇异扰动双谐波问题的各向异性误差分析

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-11 DOI:arxiv-2409.07217

Aayushman Raina, Srinivasan Natesan, Şuayip Toprakseven

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引用次数: 0

摘要

我们考虑在一个具有箝位边界条件的单位正方形域上对奇异扰动比谐椭圆问题进行弱 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 $H^{2}-$ 准则的误差估计，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。

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Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems

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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arXiv - MATH - Numerical Analysis

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