Stokes问题的可扩展局部并行双网格有限元格式

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design Pub Date : 2025-09-08 DOI:10.1016/j.finel.2025.104375

Hongwei Song , Jianping Zhao , Yanren Hou

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引用次数: 0

摘要

利用双网格法和单元分裂技术，提出了一种求解Stokes问题的局部并行有限元算法。该创新算法具有以下几个关键优势：(1)它独立于超逼近性质运行，增强了其在各种场景中的适用性；(2)区域分解完全依赖于单元分裂技术，简化了计算过程；(3)通过对局部修正的约束，该算法采用Stokes问题的惩罚形式。这种策略选择有助于在特定假设下对速度场函数进行独家解析，从而简化求解过程并可能降低计算复杂性。

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An expandable local and parallel two-grid finite element scheme for Stokes problem

A novel locally parallel finite element algorithm for addressing the Stokes problem has been developed, leveraging the two-grid method and the unit splitting technique. This innovative algorithm boasts several key advantages: (1) it operates independently of the hyperapproximation property, enhancing its applicability across various scenarios; (2) the decomposition of regions is solely dependent on the unit splitting technique, simplifying the computational process; and (3) by incorporating constraints on local corrections, the algorithm employs the penalized form of the Stokes problem. This strategic choice facilitates the exclusive resolution of the velocity field function under specific assumptions, thereby streamlining the solution process and potentially reducing computational complexity.

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来源期刊

Finite Elements in Analysis and Design 工程技术-力学

CiteScore

4.80

自引率

3.20%

发文量

审稿时长

27 days

期刊介绍： The aim of this journal is to provide ideas and information involving the use of the finite element method and its variants, both in scientific inquiry and in professional practice. The scope is intentionally broad, encompassing use of the finite element method in engineering as well as the pure and applied sciences. The emphasis of the journal will be the development and use of numerical procedures to solve practical problems, although contributions relating to the mathematical and theoretical foundations and computer implementation of numerical methods are likewise welcomed. Review articles presenting unbiased and comprehensive reviews of state-of-the-art topics will also be accommodated.