Optimal error estimates in the DG method for nonlinear convection-diffusion problems

• ID: 2547, RIV: 10027232
• ISSN: not specified, ISBN: 978-80-227-3032-7
• source: Algoritmy 2009, 18th Conference on Scientific Computing
• keywords: Optimal; error; estimates; method; nonlinear; convection-diffusion; problems
• authors: Václav Kučera
• authors from KNM: Kučera Václav

Abstract

The subject of the paper is the derivation of optimal error estimates for the discontiuous Galerkin space semi-discretization of a convection-diffusion problem with nonlinear convection and diffusion. The analysis is based on a nonlinear variant of the Aubin-Nitsche technique, which uses a linearized dual problem. Handling the nonlinearity requires several important assumptions, such as a high regularity of the exact solution, convexity of the domain and the use of only Dirichlet boundary conditions.