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Volume 33, Issue 4
A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem

Baiju Zhang & Zhimin Zhang

DOI: 10.4208/cicp.OA-2022-0216

Commun. Comput. Phys., 33 (2023), pp. 1069-1089.

Published online: 2023-05

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  • 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.

  • Keywords

Quad-curl problem, nonconforming finite element method.

  • AMS Subject Headings

65N30, 65N15, 41A25

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-33-1069, author = {Zhang , Baiju and Zhang , Zhimin}, title = {A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem}, journal = {Communications in Computational Physics}, year = {2023}, volume = {33}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0216}, url = {http://global-sci.org/intro/article_detail/cicp/21669.html} }
TY - JOUR T1 - A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem AU - Zhang , Baiju AU - Zhang , Zhimin JO - Communications in Computational Physics VL - 4 SP - 1069 EP - 1089 PY - 2023 DA - 2023/05 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0216 UR - https://global-sci.org/intro/article_detail/cicp/21669.html KW - Quad-curl problem, nonconforming finite element method. AB -

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.

Baiju Zhang & Zhimin Zhang. (2023). A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem. Communications in Computational Physics. 33 (4). 1069-1089. doi:10.4208/cicp.OA-2022-0216
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