Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems

摘要

In this paper, we discuss the superconvergence of the local discontinuous Galerkin methods for nonlinear convection-diffusion equations. We prove that the numerical solution is (k + 3/2)th-order superconvergent to a particular projection of the exact solution, when the upwind flux and the alternating fluxes are used. The proof is valid for arbitrary nonuniform regular meshes and for piecewise polynomials of degree k (k ≥ 1). The numerical experiments reveal that the property of superconvergence actually holds true for general fluxes.