Developing Stabilizer Free Weak Galerkin finite element method for second-order wave equation

Abstract

In this paper, the supercloseness property for a stabilizer free weak Galerkin (SFWG) finite element method is discussed which can be applied to solve second order wave equation. This SFWG method works as an alternative of standard weak Galerkin method. An unconditionally stable second order Newmark scheme is adopted to analyze the fully discrete scheme, whereas the spatial discretization is analyzed by the SFWG finite element. From this method, we have obtained a convergence rate which is two orders higher than the optimal convergence rate in L∞(L2) norm for the corresponding WG solution, i.e.O(hk+3+τ2). This result proves the supercloseness of two orders associated with SFWG space (Pk(K),Pk+1(∂K),[Pk+1(K)]2). Numerical experiments demonstrated here confirms the theoretical finding, robustness, and accuracy of the proposed method.