A posteriori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations

We present an a posteriori error analysis of the fully discretized time-dependent Darcy and Stokes equations, that models laminar fluid flow over a porous medium in two- or three-dimensional connected open domains which are coupled via appropriate matching conditions on the interface. The problem is discretized by the backward Euler scheme in time and finite elements in space.