A posteriori error analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem

We present and analyze an a posteriori error estimator for a space-time hybridizable discontinuous Galerkin discretization of the time-dependent advection-diffusion problem. The residual-based error estimator is proven to be reliable and locally efficient. In the reliability analysis we combine a Peclet-robust coercivity type result and a saturation assumption, while local efficiency analysis is based on using bubble functions. The analysis considers both local space and time adaptivity and is verified by numerical simulations on problems which include boundary and interior layers.