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

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  • Université Paris-Saclay
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Original languageEnglish
Pages (from-to)185-214
Number of pages30
JournalComputational Methods in Applied Mathematics
Volume24
Issue number1
Early online date31 May 2023
Publication statusPublished - 1 Jan 2024

Abstract

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.

Keywords

    Dual-Weighted Residuals, Dynamically Changing Meshes, Incompressible Navier-Stokes Equations, Mesh Adaptivity, Tensor-Product Space-Time Finite Elements

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Tensor-Product Space-Time Goal-Oriented Error Control and Adaptivity with Partition-of-Unity Dual-Weighted Residuals for Nonstationary Flow Problems. / Roth, Julian; Thiele, Jan Philipp; Köcher, Uwe et al.
In: Computational Methods in Applied Mathematics, Vol. 24, No. 1, 01.01.2024, p. 185-214.

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abstract = "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.",
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