Towards a posteriori error estimators for realistic problems in incompressible miscible displacement

The incompressible miscible displacement problem has attracted interest in recent years as it models economically important activities such as oil recovery and groundwater flow. It is important that numerical simulations can accurately model the types of problems seen in industry. We discuss a posteriori finite element indicators for the incompressible miscible displacement problem and propose an extension to a mixed-discontinuous Galerkin scheme. Furthermore we highlight some physically realistic scenarios not covered by the existing analysis and outline the theory of weighted spaces required to address them.