Space-Time Goal Oriented Error Estimation and Adaptivity for Discretization and Reduced Order Modeling Errors

In this presentation, we present a uniform framework in which the dual-weighted residual (DWR) method is used for spatial and temporal discretization error control [1], as well as the control of the reduced order modeling error for the proper orthogonal decomposition (POD). In the first part of this presentation, the DWR method is applied to a space-time formulation of non-stationary Navier-Stokes flow. Tensor-product space-time finite elements are being used to discretize the variational formulation with discontinuous Galerkin finite elements in time and inf-sup stable Taylor-Hood finite element pairs in space. To estimate the error in a quantity of interest and drive adaptive refinement in time and space, we demonstrate how the DWR method for incompressible flow [2] can be extended to a partition of unity based error localization [3, 4]. Our methodology is being substantiated on the two dimensional flow around a cylinder benchmark problem. In the second