On the superconvergence of a WG method for the elliptic problem with variable coefficients

This article extends a recently developed superconvergence result for weak Galerkin (WG) approximations for modeling partial differential equations from constant coefficients to variable coefficients. This superconvergence features a rate that is two-order higher than the optimal-order error estimates in the usual energy and L2 norms. The extension from constant to variable coefficients for the modeling equations is highly non-trivial. The underlying technical analysis is based on the use of a sequence of projections and decompositions. Numerical results are presented to confirm the superconvergence theory for second-order elliptic problems with variable coefficients.