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 - <p style="text-align: justify;">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.</p>