Weak Galerkin finite element methods for quad-curl problems

This article introduces a weak Galerkin (WG) finite element method for quad-curl problems in three dimensions. It is proved that the proposed WG method is stable and accurate in an optimal order of error estimates for the exact solution in discrete norms. In addition, an L2 error estimate in an opti...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 428; p. 115186
Main Authors Wang, Chunmei, Wang, Junping, Zhang, Shangyou
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.08.2023
Subjects
Finite element methods
Polyhedral partition
Quad-curl problem
Weak Galerkin
secondary
WG
Polyhedral partition
Quad-curl problem
Weak Galerkin
Finite element methods
primary
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ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2023.115186

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Summary:This article introduces a weak Galerkin (WG) finite element method for quad-curl problems in three dimensions. It is proved that the proposed WG method is stable and accurate in an optimal order of error estimates for the exact solution in discrete norms. In addition, an L2 error estimate in an optimal order except the lowest order k=2 is derived for the WG solution. Some numerical experiments are conducted to verify the efficiency and accuracy of our WG method and furthermore a superconvergence has been observed from the numerical results.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2023.115186