Accepted

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

Chunyu Chen, Long Chen, Xuehai Huang, Huayi Wei

Communications in Computational Physics

arXiv   Bibtex

ABSTRACT:

This paper delves into the world of high-order curl and div
elements within finite element methods, providing valuable insights
into their geometric properties, indexing management, and practical
implementation considerations. It first explores the decomposition of
Lagrange finite elements. The discussion then extends to
H(div)-conforming finite elements and H(curl)-conforming finite
element spaces by choosing different frames at different
sub-simplex. The required tangential continuity or normal continuity
will be imposed by appropriate choices of the tangential and normal
basis. 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 in the realm
of high-order curl and div elements in finite element methods, which
are vital for solving vector field problems and understanding
electromagnetic phenomena.