Year: 2020
Author: Qian Zhang, Zhimin Zhang
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 4 : pp. 639–663
Abstract
In [23], we, together with our collaborator, proposed a family of $H$(curl$^2$)- conforming elements on both triangular and rectangular meshes. The elements provide a brand new method to solve the quad-curl problem in 2 dimensions. In this paper, we turn our focus to 3 dimensions and construct $H$(curl$^2$)-conforming finite elements on tetrahedral meshes. The newly proposed elements have been proved to have the optimal interpolation error estimate. Having the tetrahedral elements, we can solve the quad-curl problem in any Lipschitz domain by the conforming finite element method. We also provide several numerical examples of using our elements to solve the quad-curl problem. The results of the numerical experiments show the correctness of our elements.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0023
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 4 : pp. 639–663
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: $H^2$(curl)-conforming finite elements tetrahedral mesh quad-curl problems interpolation errors convergence analysis.
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