A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to $\boldsymbol{u_t}$+$\boldsymbol{u_x}$=0

Abstract

The superconvergent property of the Discontinuous Galerkin (DG) method for linear hyperbolic systems of partial differential equations in one dimension is explained by relating the DG method to a particular continuous method, whose accuracy depends in part on a local analysis, and in part on information transferred from upwind elements.