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Volume 16, Issue 2
Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media

Bhupen Deka, Papri Roy, Naresh Kumar & Raman Kumar

DOI: 10.4208/nmtma.OA-2021-0080

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 323-347.

Published online: 2023-04

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  • Abstract

Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space $(\mathcal{P}_k(K), \mathcal{P}_{k−1}(∂K), [\mathcal{P}_{k−1}(K)]^2).$ Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in $L^∞(L^2)$ norm. This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes. Finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.

  • Keywords

Wave equation, heterogeneous medium, finite element method, weak Galerkin method, semidiscrete and fully discrete schemes, optimal error estimates.

  • AMS Subject Headings

65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-16-323, author = {Deka , BhupenRoy , PapriKumar , Naresh and Kumar , Raman}, title = {Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {2}, pages = {323--347}, abstract = {

Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space $(\mathcal{P}_k(K), \mathcal{P}_{k−1}(∂K), [\mathcal{P}_{k−1}(K)]^2).$ Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in $L^∞(L^2)$ norm. This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes. Finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0080}, url = {http://global-sci.org/intro/article_detail/nmtma/21579.html} }
TY - JOUR T1 - Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media AU - Deka , Bhupen AU - Roy , Papri AU - Kumar , Naresh AU - Kumar , Raman JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 323 EP - 347 PY - 2023 DA - 2023/04 SN - 16 DO - http://doi.org/10.4208/nmtma.OA-2021-0080 UR - https://global-sci.org/intro/article_detail/nmtma/21579.html KW - Wave equation, heterogeneous medium, finite element method, weak Galerkin method, semidiscrete and fully discrete schemes, optimal error estimates. AB -

Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space $(\mathcal{P}_k(K), \mathcal{P}_{k−1}(∂K), [\mathcal{P}_{k−1}(K)]^2).$ Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in $L^∞(L^2)$ norm. This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes. Finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.

Deka , BhupenRoy , PapriKumar , Naresh and Kumar , Raman. (2023). Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media. Numerical Mathematics: Theory, Methods and Applications. 16 (2). 323-347. doi:10.4208/nmtma.OA-2021-0080
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