RESIDUAL BASED ERROR ESTIMATES FOR THE SPACE-TIME DISCONTINUOUS GALERKIN METHOD APPLIED TO NONLINEAR HYPERBOLIC EQUATIONS

We present an adaptive numerical method for solving nonlinear hyperbolic equations. The method uses the space-time discontinuous Galerkin discretization, exploiting its high polynomial approximation degrees with respect to both space and time coordinates. We derive an residual based a posteriori error estimator and propose an efficient strategy how to identify the parts of the computational error caused by the space and time discretization, respectively, as well as the errors arising from the linearization of the resultant algebraic system of equations. Further, an algorithm keeping all these three components of the computational error balanced is presented. The computational performance of the proposed method is demonstrated by numerical experiments.