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In this work, a cost-efficient space-time adaptive algorithm based on theDual Weighted Residual (DWR) method is developed and studied for a coupledmodel problem of flow and convection-dominated transport. Key ingredients are amultirate approach adapted to varying dynamics in time of the subproblems,weighted and non-weighted error indicators for the transport and flow problem,respectively, and the concept of space-time slabs based on tensor productspaces for the data structure. In numerical examples the performance of theunderlying algorithm is studied for benchmark problems and applications ofpractical interest. Moreover, the interaction of stabilization andgoal-oriented adaptivity is investigated for strongly convection-dominatedtransport.

A Cost-Efficient Space-Time Adaptive Algorithm for Coupled Flow and Transport