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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.

Keywords

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