Stability analysis of the space-time discontinuous Galerkin method for nonstationary nonlinear convection-diffusion problems

Abstract

This paper is concerned with the stability analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty.

Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method.

Theoretical results are demonstrated by a numerical example.

Keywords

• Stability analysis
• space-time discontinuous Galerkin method
• nonstationary nonlinear convection-diffusion problems