非凸多边形网格上Stokes方程的自稳定弱Galerkin有限元方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics Pub Date : 2025-04-14 DOI:10.1016/j.jcp.2025.114006

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伽辽金（WG）有限元法，用于求解Stokes方程而不依赖于传统的稳定器。提出的WG方法在有限元分区中容纳凸和非凸多边形元素，利用气泡函数作为关键的分析工具。简化后的WG方法是对称的和正定的，并在离散H1范数和L2范数下导出了WG近似的最优阶误差估计。

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

Auto-stabilized weak Galerkin finite element methods for Stokes equations on non-convex polytopal meshes

This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for solving Stokes equations without relying on traditional stabilizers. The proposed WG method accommodates both convex and non-convex polytopal elements in finite element partitions, leveraging bubble functions as a key analytical tool. The simplified WG method is symmetric and positive definite, and optimal-order error estimates are derived for WG approximations in both the discrete

H^{1}

norm and the

L^{2}

norm.

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来源期刊

Journal of Computational Physics 物理-计算机：跨学科应用

CiteScore

7.60

自引率

14.60%

发文量

763

审稿时长

5.8 months

期刊介绍： Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.