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Weak Galerkin finite element methods for semilinear Klein–Gordon equation on polygonal meshes

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Abstract

The article presents the development of the weak Galerkin finite element method (WG-FEM) for semilinear hyperbolic problems. Semidiscrete error estimate in \(L^2\)-norm as well as \(H^1\)-norm have been executed for the weak Galerkin space \(({\textbf{P}}_k ({\mathcal {K}}), {\textbf{P}}_{k} (\partial {\mathcal {K}}), [{\textbf{P}}_{k-1} ({\mathcal {K}})]^2),\) where \(k \ge 1\) is an integer. For a fully discrete scheme, we employ the Newmark scheme for temporal discretization. Finally, a few numerical results are provided to validate theoretical results.

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Acknowledgements

Authors are grateful to the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Guwahati, North Guwahati, Guwahati, 781039, India

    Puspendu Jana, Naresh Kumar & Bhupen Deka

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  1. Puspendu Jana
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  2. Naresh Kumar
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  3. Bhupen Deka
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Correspondence to Bhupen Deka.

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Jana, P., Kumar, N. & Deka, B. Weak Galerkin finite element methods for semilinear Klein–Gordon equation on polygonal meshes. Comp. Appl. Math. 43, 218 (2024). https://doi.org/10.1007/s40314-024-02745-z

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  • DOI: https://doi.org/10.1007/s40314-024-02745-z

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