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.