非凸网格弹性界面问题的自稳定弱Galerkin方法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-06-23 DOI:10.1016/j.cam.2025.116854

Chunmei Wang , Shangyou Zhang

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引用次数: 0

摘要

本文介绍了一种自稳定弱Galerkin （WG）有限元方法，用于一般多边形和多面体网格的弹性界面问题，不需要凸性约束。该方法利用气泡函数作为关键的分析工具，消除了传统WG方法中通常使用的稳定剂的需要，从而使配方更加精简。该方法具有对称、正定、易于实现等特点。假设精确解具有足够的平滑性，为离散h1范数中的WG近似导出了最优阶误差估计。数值实验验证了该方法的准确性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An auto-stabilized weak Galerkin method for elasticity interface problems on nonconvex meshes

This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for elasticity interface problems on general polygonal and polyhedral meshes, without requiring convexity constraints. The method utilizes bubble functions as key analytical tools, eliminating the need for stabilizers typically used in traditional WG methods and leading to a more streamlined formulation. The proposed method is symmetric, positive definite, and easy to implement. Optimal-order error estimates are derived for the WG approximations in the discrete

H^{1}

-norm, assuming the exact solution has sufficient smoothness. Numerical experiments validate the accuracy and efficiency of the auto-stabilized WG method.

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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.