Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-10-15 DOI:10.1016/j.cam.2024.116324

Shicheng Liu , Xiangyun Meng , Qilong Zhai

引用次数: 0

Abstract

In this paper, we apply the weak Galerkin (WG) finite element method to solve the singularly perturbed fourth-order boundary value problem in a 2D domain. A Shishkin mesh is used to ensure that the method exhibits uniform convergence, regardless of the singular perturbation parameter. Asymptotically optimal order error estimate in a

H^{2}

discrete norm is established for the corresponding WG solutions. Numerical tests are provided to verify the convergence theory.

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针对二维奇异扰动四阶问题的 Shishkin 网格弱 Galerkin 有限元方法的收敛性分析

本文采用弱 Galerkin（WG）有限元法求解二维域中的奇异扰动四阶边界值问题。我们使用 Shishkin 网格来确保该方法表现出均匀的收敛性，而不受奇异扰动参数的影响。为相应的 WG 解建立了 H2 离散规范下的渐近最优阶误差估计。提供了数值测试来验证收敛理论。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.