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Mathematics > Numerical Analysis

arXiv:2308.02873 (math)
[Submitted on 5 Aug 2023]

Title:A Modified weak Galerkin finite element method for the Maxwell equations on polyhedral meshes

Authors:Chunmei Wang, Xiu Ye, Shangyou Zhang
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Abstract: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.
Comments: 19 pages, 4 tables
Subjects: Numerical Analysis (math.NA)
MSC classes: 65N15, 65N30, 76D07
Cite as: arXiv:2308.02873 [math.NA]
  (or arXiv:2308.02873v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2308.02873

Submission history

From: Chunmei Wang [view email]
[v1] Sat, 5 Aug 2023 12:58:05 UTC (412 KB)
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