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 - <p style="text-align: justify;">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.</p>