A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to $\boldsymbol{u_t}$+$\boldsymbol{u_x}$=0 (Communications in Computational Physics, 2018)
The superconvergent property of the Discontinuous Galerkin (DG) methodfor linear hyperbolic systems of partial differential equations in one dimension is explainedby relating the DG method to a particular continuous method, whose accuracydepends in part on a local analysis, and in part on information transferred from upwindelements.