A modified weak Galerkin finite element method for the Maxwell equations on polyhedral meshes

We introduce a new numerical method for solving time-harmonic Maxwell’s equations via the modified weak Galerkin technique. The inter-element functions of the weak Galerkin finite elements are replaced by the average of the two discontinuous polynomial functions on the two sides of the polygon, in t...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 448; p. 115918
Main Authors Wang, Chunmei, Ye, Xiu, Zhang, Shangyou
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2024
Subjects
Finite element methods
Maxwell equations
Modified weak Galerkin
Polyhedral meshes
Weak curl
secondary
Modified weak Galerkin
Polyhedral meshes
Weak curl
Finite element methods
Maxwell equations
primary
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ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2024.115918

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Summary:We introduce a new numerical method for solving time-harmonic Maxwell’s equations via the modified weak Galerkin technique. The inter-element functions of the weak Galerkin finite elements are replaced by the average of the two discontinuous polynomial functions on the two sides of the polygon, in the modified weak Galerkin (MWG) finite element method. With the dependent inter-element functions, the weak curl and the weak gradient are defined directly on totally discontinuous polynomials. Optimal-order convergence of the method is proved. Numerical examples confirm the theory and show effectiveness of the modified weak Galerkin method over the existing methods.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2024.115918