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Mathematics > Numerical Analysis

arXiv:2210.16612 (math)
[Submitted on 29 Oct 2022]

Title:Weak Galerkin Finite Element Methods for Quad-Curl Problems

Authors:Chunmei Wang, Junping Wang, Shangyou Zhang
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Abstract: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 $L^2$ error estimate in an optimal order except the lowest orders $k=1, 2$ 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.
Comments: 16 pages, 2 tables
Subjects: Numerical Analysis (math.NA)
MSC classes: 65N30, 65N15, 65N12
Cite as: arXiv:2210.16612 [math.NA]
  (or arXiv:2210.16612v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2210.16612

Submission history

From: Chunmei Wang [view email]
[v1] Sat, 29 Oct 2022 14:30:20 UTC (26 KB)
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