An adaptive hp-discontinuous Galerkin approach for nonlinear convection-diffusion problems

Abstract

We deal with a numerical solution of nonlinear convection-diffusion equations with the aid of the discontinuous Galerkin method. We propose a new hp-adaptation technique, which is based on a combination of a residuum estimator and a regularity indicator.

Keywords

• adaptive hp-discontinuous Galerkin method
• nonlinear convection-diffusion problems
• residual error indicators