Superconvergence of Discontinuous Galerkin Method for Nonstationary Hyperbolic Equation

Abstract

For the first order nonstationary hyperbolic equation taking the piecewise linear discontinuous Galerkin solver, we prove that under the uniform rectangular partition, such a discontinuous solver, after postprocessing, can have two and a half approximative order which is half order higher than the optimal estimate by Lesaint and Raviart under the rectangular partition.