Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media

Weak Galerkin finite element method is introduced for solving wave equa-tion with interface on weak Galerkin finite element space (Pk(K), Pk-1( partial differential K), [Pk-1(K)]2). Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in L infinity(L2) 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.