Distributional Finite Element curl div Complexes and Application to Quad Curl Problems

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-05-14 DOI:10.1137/23m1617400

Long Chen, Xuehai Huang, Chao Zhang

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1078-1104, June 2025.
Abstract. This paper addresses the challenge of constructing finite element [math] complexes in three dimensions. Tangential-normal continuity is introduced in order to develop distributional finite element [math] complexes. The spaces constructed are applied to discretize the quad curl problem, demonstrating optimal order of convergence. Furthermore, a hybridization technique is proposed, demonstrating its equivalence to nonconforming finite elements and weak Galerkin methods.

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分布有限元旋度复形及其在四旋度问题中的应用

SIAM数值分析杂志，第63卷，第3期，1078-1104页，2025年6月。摘要。本文解决了在三维空间中构造有限元[数学]复合体的挑战。为了发展分布有限元[数学]复合体，引入了切法连续。将所构造的空间用于离散四旋度问题，证明了其最优收敛阶。此外，提出了一种杂交方法，证明了它与非协调有限元和弱伽辽金方法的等价性。

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

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.