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 st...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 24; no. 1; pp. 185 - 214
Main Authors Roth, Julian, Thiele, Jan Philipp, Köcher, Uwe, Wick, Thomas
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.01.2024
Walter de Gruyter GmbH
Subjects
65N30
65N50
76D05
Dual-Weighted Residuals
Dynamically Changing Meshes
Errors
Fluid flow
Fluid mechanics
Incompressible flow
Incompressible Navier–Stokes Equations
Mathematics
Mesh Adaptivity
Stokes flow
Tensor-Product Space-Time Finite Elements
Tensors
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ISSN1609-4840
1609-9389
DOI10.1515/cmam-2022-0200

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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 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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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2022-0200