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In this work, the dual-weighted residual method is applied to a space-timeformulation of nonstationary Stokes and Navier-Stokes flow. Tensor-productspace-time finite elements are being used to discretize the variationalformulation with discontinuous Galerkin finite elements in time and inf-supstable Taylor-Hood finite element pairs in space. To estimate the error in aquantity of interest and drive adaptive refinement in time and space, wedemonstrate how the dual-weighted residual method for incompressible flow canbe extended to a partition of unity based error localization. We derive thespace-time Newton method for the Navier-Stokes equations and substantiate ourmethodology on 2D benchmark problems from computational fluid mechanics.

Tensor-product space-time goal-oriented error control and adaptivity with partition-of-unity dual-weighted residuals for nonstationary flow problems