Nonconforming Finite Elements for the -curlΔcurl and Brinkman Problems on Cubical Meshes
Document Type
Article
Publication Date
12-2023
Department
Department of Mathematical Sciences
Abstract
We propose two families of nonconforming elements on cubical meshes: one for the -curlΔcurl problem and the other for the Brinkman problem. The element for the -curlΔcurl problem is the first nonconforming element on cubical meshes. The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the viscosity coefficient v. The lowest-order elements for the -curlΔcurl and the Brinkman problems have 48 and 30 DOFs on each cube, respectively. The two families of elements are subspaces of H(curl;Ω) and H(div;Ω), and they, as nonconforming approximation to H(gradcurl;Ω) and [H1(Ω)]3, can form a discrete Stokes complex together with the serendipity finite element space and the piecewise polynomial space.
Publication Title
Communications in Computational Physics
Recommended Citation
Zhang, Q.,
Zhang, M.,
&
Zhang, Z.
(2023).
Nonconforming Finite Elements for the -curlΔcurl and Brinkman Problems on Cubical Meshes.
Communications in Computational Physics,
34(5), 1332-1360.
http://doi.org/10.4208/cicp.OA-2023-0102
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/315