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

arXiv: https://arxiv.org/abs/2210.02965 · HTML: https://mlsanity.com/paper/2210.02965/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamics](https://mlsanity.com/paper/2408.06101/) (2024)

## Abstract (arXiv)

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 derive the space-time Newton method for the Navier-Stokes equations and substantiate our methodology on 2D benchmark problems from computational fluid mechanics.