Three families of grad-div-conforming finite elements
Numerical Analysis
2020-07-22 v1 Numerical Analysis
Abstract
Several smooth finite element de Rham complexes are constructed in three-dimensional space, which yield three families of grad-div conforming finite elements. The simplest element has only 8 degrees of freedom (DOFs) for a tetrahedron and 14 DOFs for a cuboid. These elements naturally lead to conforming approximations to quad-div problems. Numerical experiments for each family validate the correctness and efficiency of the elements for solving the quad-div problem.
Cite
@article{arxiv.2007.10856,
title = {Three families of grad-div-conforming finite elements},
author = {Qian Zhang and Zhimin Zhang},
journal= {arXiv preprint arXiv:2007.10856},
year = {2020}
}
Comments
28 pages; 6 figures. arXiv admin note: text overlap with arXiv:2004.12507