Flexible goal-oriented space-time adaptivity for coupled Stokes flow and convection-dominated transport

In this work, a flexible, fully space-time adaptive finite element approximation of a prototype multi-physics system coupling fluid flow and convection-dominated transport is developed and studied. By some minor generalization, the model becomes feasible for the simulation of a poroelasticity system. Automatic mesh adaptation is based on the Dual Weighted Residual method for goal-oriented a posteriori error estimation. In multi-physics, the reliable and economical computation of a specific functional, the so-called quantity of interest, is typically desirable. Here, adaptive algorithms become more involved since they need not only to control the time and space meshes, but also need to balance the contributions of the coupled subproblems to the error in the goal quantity. Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of effects of temporal and spatial discretization which facilitates the simultaneous adjustment of the time and space mesh.