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Volume 35, Issue 4
Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements

Chunyu Chen, Long Chen, Xuehai Huang & Huayi Wei

DOI: 10.4208/cicp.OA-2023-0249

Commun. Comput. Phys., 35 (2024), pp. 1045-1072.

Published online: 2024-05

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  • 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.

  • Keywords

Implementation of finite elements, nodal finite elements, $H$(curl)-conforming, $H$(div)-conforming.

  • AMS Subject Headings

65N30, 35Q60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-35-1045, author = {Chen , ChunyuChen , LongHuang , Xuehai and Wei , Huayi}, title = {Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements}, journal = {Communications in Computational Physics}, year = {2024}, volume = {35}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/ 10.4208/cicp.OA-2023-0249}, url = {http://global-sci.org/intro/article_detail/cicp/23094.html} }
TY - JOUR T1 - Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements AU - Chen , Chunyu AU - Chen , Long AU - Huang , Xuehai AU - Wei , Huayi JO - Communications in Computational Physics VL - 4 SP - 1045 EP - 1072 PY - 2024 DA - 2024/05 SN - 35 DO - http://doi.org/ 10.4208/cicp.OA-2023-0249 UR - https://global-sci.org/intro/article_detail/cicp/23094.html KW - Implementation of finite elements, nodal finite elements, $H$(curl)-conforming, $H$(div)-conforming. AB -

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.

Chunyu Chen, Long Chen, Xuehai Huang & Huayi Wei. (2024). Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements. Communications in Computational Physics. 35 (4). 1045-1072. doi: 10.4208/cicp.OA-2023-0249
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