Superconvergent weak Galerkin methods for non-self adjoint and indefinite elliptic problems

Abstract In this paper we present a stabilizer-free weak Galerkin (SFWG) finite element scheme for the approximation of the non-self adjoint and indefinite elliptic equations. Supercloseness convergence of the SFWG method is derived. After a suitable postprocessing of the SFWG solution, the resulting post-processed solution converges with two order higher than the optimal order in both H 1 semi-norm and L 2 norm on triangular meshes. Numerical experiments are demonstrated to verify the theoretical findings.