  In this work, a flexible higher-order space-time adaptive finite element
approximation of convection-dominated transport with coupled fluid flow is
developed and studied. Convection-dominated transport is a challenging
subproblem in poromechanics in which coupled transport with flow, chemical
reaction and mechanical response in porous media is considered. Key ingredients
are the arbitrary degree discontinuous Galerkin time discretization of the
primal and dual problems for the Dual Weighted Residual (DWR) approach, an a
posteriori error estimation for the transport problem coupled with flow and its
implementation in an advanced software architecture. The error estimate allows
the separation of the temporal and spatial discretization error contributions
which facilitates the simultaneous adjustment of the time and space mesh. The
performance of the approach and its software implementation is studied by
numerical convergence examples as well as an example of physical interest for
convection-dominated cases.
