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

• ID: 2710, RIV: 10317210
• ISSN: not specified, ISBN: 978-80-85823-64-6
• source: Programs and Algorithms of Numerical mathematics 17
• keywords: discontinuous Galerkin method; Runge-Kutta method; a priori error analysis; superconvergence
• authors: Miloslav Vlasák, Filip Roskovec
• authors from KNM: Roskovec Filip

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.