An improved superconvergence error estimate for the LDG method

In this manuscript we present an error analysis for the local discontinuous Galerkin method for a model elliptic problem on Cartesian meshes when polynomials of degree at most k   and an appropriate approximation of the boundary condition are used. This special approximation allows us to achieve k+1k+1 order of convergence for both the potential and its gradient in the L2L2 norm. Here we improve on existing estimates for the solution gradient by a factor h.