On Runge-Kutta, collocation and discontinuous Galerkin methods: mutual connections and resulting consequences to the analysis

Abstract

It is shown that discontinuous Galerkin method has natural mutual connection to collocation methods and Runge-Kutta methods. This connection enables us to employ the techniques of proofs developed for any of these methods.

We use this idea to discuss the superconvergence property for discontinuous Galerkin method.

Keywords

• discontinuous Galerkin method
• Runge-Kutta method
• a priori error analysis
• superconvergence