Year: 2024
Author: Chunyu Chen, Long Chen, Xuehai Huang, Huayi Wei
Communications in Computational Physics, Vol. 35 (2024), Iss. 4 : pp. 1045–1072
Abstract
This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange finite elements, setting the foundation for further analysis. The discussion then extends to $H$(div)-conforming and $H$(curl)-conforming finite element spaces, adopting variable frames across differing sub-simplices. The imposition of tangential or normal continuity is achieved through the strategic selection of corresponding bases. The paper concludes with a focus on efficient indexing management strategies for degrees of freedom, offering practical guidance to researchers and engineers. It serves as a comprehensive resource that bridges the gap between theory and practice.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0249
Communications in Computational Physics, Vol. 35 (2024), Iss. 4 : pp. 1045–1072
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Implementation of finite elements nodal finite elements $H$(curl)-conforming $H$(div)-conforming.