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

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