Superconvergence of DG Method for a Class of General Hyperbolic Equations with Periodic Boundary Conditions

Abstract

This paper studies the discontinuous Galerkin (DG) method for a class of general hyperbolic equations with periodic boundary conditions when upwind fluxes are used. By constructing a improved correction function and interpolation function, for any polynomial degree k superconvergence of the point-wise and element average error estimates are derived.