Discontinuous Galerkin method for the solution of a transport level-set problem

• ID: 2719, RIV: 10325036
• ISSN: 0898-1221, ISBN: not specified
• source: Computers and Mathematics with Applications
• keywords: Discontinuous Galerkin method; transport level-set problém; error estimates; numerical experiments
• authors: Eva Bezchlebová, Vít Dolejší, Miloslav Feistauer
• authors from KNM: Dolejší Vít, Feistauer Miloslav

Abstract

The subject of the paper is the numerical analysis of the transport level-set problem discretized by the discontinuous Galerkin method. Without the assumption that the first order nonstationary transport equation contains a reaction term, which is used in a standard literature, we prove error estimates in the Loo(L2)-norm in the case of the space semidiscretization method of lines and in the case of the space-time discontinuous Galerkin method in the L2(L2)-norm. Numerical experiments support the derived error estimates and show that they are not sharp in the case of the space-time discontinuous Galerkin method.