A priori error estimates of an extrapolated space-time discontinuous Galerkin method for nonlinear convection-diffusion problems

Abstract

The paper deals with the numerical solution of a scalar nonstationary nonlinear convection-diffusion equation. We employ a combination of the discontinuous Galerkin finite element method for the space as well as time discretization.

We analyze this scheme and derive a priori asymptotic error estimates. Finally, we present an efficient solution strategy and numerical examples verifying the theoretical results

Keywords

• a priori error estimates
• extrapolated space-time discontinuous Galerkin method
• nonlinear convection-diffusion problem