Adaptive hybridizable discontinuous Galerkin methods for nonstationary convection diffusion problems

Abstract

This work is concerned with adaptive hybridizable discontinuous Galerkin methods of nonstationary convection diffusion problems. We address first the spatially semidiscrete case and then move to the fully discrete scheme by introducing a backward Euler discretization in time. More specifically, the computable a posteriori error estimator for the time-dependent problem is obtained by using the idea of elliptic reconstruction and conforming-nonconforming decomposition. In view of the method that has been employed in the time-dependent problem, we also obtain a computable a posteriori error estimator for the fully discrete scheme. Finally, two examples show the performance of the obtained a posteriori error estimators.