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A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem

A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem
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Year:    2023

Author:    Baiju Zhang, Zhimin Zhang

Communications in Computational Physics, Vol. 33 (2023), Iss. 4 : pp. 1069–1089

Abstract

We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem. The proposed finite element spaces are subspaces of $\boldsymbol{H}$(curl), but not of $\boldsymbol{H}$(grad curl), which are different from the existing nonconforming ones [10,12,13]. The well-posedness of the discrete problem is proved and optimal error estimates in discrete $\boldsymbol{H}$(grad curl) norm, $\boldsymbol{H}$(curl) norm and $L^2$ norm are derived. Numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2022-0216

Communications in Computational Physics, Vol. 33 (2023), Iss. 4 : pp. 1069–1089

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Quad-curl problem nonconforming finite element method.

Author Details

Baiju Zhang

Zhimin Zhang

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