Tensor-Product Space-Time Goal-Oriented Error Control and Adaptivity With Partition-of-Unity Dual-Weighted Residuals for Nonstationary Flow Problems

In this work, the dual-weighted residual method is applied to a space-time formulation of nonstationary Stokes and 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 dual-weighted residual method for incompressible flow can be extended to a partition-of-unity based error localization. We substantiate our methodology on 2D benchmark problems from computational fluid mechanics.

Automated summary

In this work, the dual-weighted residual method is applied to a space-time formulation of nonstationary Stokes and Navier-Stokes flow. Tensor-product space-time finite elements are used for discretization with discontinuous Galerkin finite elements in time and inf-sup stable Taylor-Hood finite element pairs in space. To estimate the error and drive adaptive refinement, a partition-of-unity based error localization is developed using the dual-weighted residual method. The methodology is validated on 2D benchmark problems from computational fluid mechanics.