A new reconstruction-enhanced discontinuous Galerkin method for time-dependent problems

• ID: 2543, RIV: 10081011
• ISSN: not specified, ISBN: 978-80-85823-57-8
• source: Programs and Algorithms of Numerical Mathematics 15
• keywords: discontinuous Galerkin; high-order reconstruction; time-dependent problems
• authors: Václav Kučera
• authors from KNM: Kučera Václav

Abstract

This work is concerned with the introduction of a new numerical scheme based on the discontinuous Galerkin (DG) method. We propose to follow the methodology of higher order finite volume schemes and introduce a reconstruction operator into the DG scheme. This operator constructs higher order piecewise polynomial reconstructions from the lower order DG scheme. Such a procedure was proposed already in Dumbser et al. (2003) based on heuristic arguments, however we provide a rigorous derivation, which justifies the increased order of accuracy. Numerical experiments are carried out.