Supercloseness and postprocessing of stabilizer-free weak Galerkin finite element approximations for parabolic problems

Abstract

In this paper we present a fully discrete stabilizer-free weak Galerkin (SFWG) finite element scheme for the approximation of the parabolic equations. The temporal variable is discretized by the second order Crank-Nicolson scheme; the spatial variables are discretized by a stabilizer-free weak Galerkin finite element method. The stability and supercloseness convergence of both the semi-discrete SFWG method and the fully discrete SFWG method have been established. A postprocessing technique is given to obtain a global superconvergence finite element approximation with two order higher than the optimal order in both H1 semi-norm and L2 norm on triangular meshes. Numerical experiments are demonstrated to verify the theoretical findings.