AN ADAPTIVE hp-DISCONTINUOUS GALERKIN APPROACH FOR NONLINEAR CONVECTION-DIFFUSION PROBLEMS

We deal with a numerical solution of nonlinear convection-diffusion equations with the aid of the discontinuous Galerkin method (DGM). We propose a new hp-adaptation technique, which is based on a combination of a residuum estimator and a regularity indicator. The residuum estimator as well as the regularity indicator are easily evaluated quantities without the necessity to solve any local problem and/or any reconstruction of the approximate solution. The performance of the proposed hp-DGM is demonstrated