Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements (Communications in Computational Physics, 2024)
This study investigates high-order face and edge elements in finite elementmethods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrangefinite elements, setting the foundation for further analysis. The discussion then extends to $H$(div)-conforming and $H$(curl)-conforming finite element spaces, adoptingvariable frames across differing sub-simplices. The imposition of tangential or normalcontinuity is achieved through the strategic selection of corresponding bases. The paper concludes with a focus on efficient indexing management strategies for degreesof freedom, offering practical guidance to researchers and engineers. It serves as acomprehensive resource that bridges the gap between theory and practice.
Keywords: Implementation of finite elements; nodal finite elements; $H$(curl)-conforming; $H$(div)-conforming.