Three families of grad div-conforming finite elements
Document Type
Article
Publication Date
11-1-2022
Department
Department of Mathematical Sciences
Abstract
Several smooth finite element de Rham complexes are constructed in three-dimensional space, which yield three families of graddiv -conforming finite elements. The simplest element has only 8 degrees of freedom (DOFs) for a tetrahedron and 14 DOFs for a 3-rectangle. We show that these elements lead to conforming and convergent approximations to quad-div problems. As a by-product, we obtain some graddiv -nonconforming elements. Numerical experiments validate the correctness and efficiency of the nonconforming elements for solving the quad-div problem.
Publication Title
Numerische Mathematik
Recommended Citation
Zhang, Q.,
&
Zhang, Z.
(2022).
Three families of grad div-conforming finite elements.
Numerische Mathematik,
152(3), 701-724.
http://doi.org/10.1007/s00211-022-01321-z
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/16427