Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements

Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements

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.

Author Details

Chunyu Chen

Long Chen

Xuehai Huang

Huayi Wei

  1. H(div)-conforming finite element tensors with constraints

    Chen, Long

    Huang, Xuehai

    Results in Applied Mathematics, Vol. 23 (2024), Iss. P.100494

    https://doi.org/10.1016/j.rinam.2024.100494 [Citations: 0]