Space-time adaptation for purely diffusive problems in an anisotropic framework

The main goal of this work is the proposal of an efficient space-time adaptive procedure for a cGdG approximation of an unsteady diffusion problem. We derive a suitable a posteriori error estimator where the contribution of the spatial and of the temporal discretization is kept distinct. In particular our interest is addressed to phenomena characterized by temporal multiscale as well as strong spatial directionalities. On the one hand we devise a sound criterion to update the time step, able to follow the evolution of the problem under investigation. On the other hand we exploit an anisotropic triangular adapted grid. The reliability and the efficiency of the proposed error estimator are assessed numerically.