Analysis of the discontinuous Galerkin finite element method applied to a scalar nonlinear convection-diffusion equation

• ID: 2449, RIV: 10118821
• ISSN: not specified, ISBN: 978-80-85823-55-4
• source: PROGRAMS AND ALGORITHMS OF NUMERICAL MATHEMATICS 14
• keywords: discontinuous Galerkin method; a priori error estimates
• authors: Vít Dolejší, Jiří Hozman
• authors from KNM: Dolejší Vít

Abstract

We deal with a scalar nonstationary convection-diffusion equation with nonlinear convective as well as diffusive terms which represents a model problem for the solution of the system of the compressible Navier-Stokes equations describing a motion of viscous compressible fluids. We present a discretization of this model equation by the discontinuous Galerkin finite element method. Moreover, under some assumptions on the nonlinear terms, domain partitions and the regularity of the exact solution, we introduce a priori error estimates. A sketch of the proof is presented.