Year: 2023
Author: Qian Zhang, Min Zhang, Zhimin Zhang
Communications in Computational Physics, Vol. 34 (2023), Iss. 5 : pp. 1332–1360
Abstract
We propose two families of nonconforming elements on cubical meshes: one for the −curl∆curl problem and the other for the Brinkman problem. The element for the −curl∆curl 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 $ν.$ The lowest-order elements for the −curl∆curl and the Brinkman problems have 48 and 30 DOFs on each cube, respectively. The two families of elements are subspaces of $H({\rm curl};Ω)$ and $H({\rm div};Ω),$ and they, as nonconforming approximation to $H({\rm gradcurl};Ω)$ and $[H^1 (Ω)]^3,$ can form a discrete Stokes complex together with the serendipity finite element space and the piecewise polynomial space.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0102
Communications in Computational Physics, Vol. 34 (2023), Iss. 5 : pp. 1332–1360
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Nonconforming elements −curl∆curl problem Brinkman problem finite element de Rham complex Stokes complex.