Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media
Year: 2023
Author: Raman Kumar, Bhupen Deka, Papri Roy, Naresh Kumar, Raman Kumar
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2021-0080
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 2 : pp. 323–347
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Wave equation heterogeneous medium finite element method weak Galerkin method semidiscrete and fully discrete schemes optimal error estimates.