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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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
Online AccessGet full text
ISSN1609-4840
1609-9389
DOI10.1515/cmam-2022-0200

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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.
AbstractList 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.
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.
Author Thiele, Jan Philipp
Roth, Julian
Köcher, Uwe
Wick, Thomas
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  organization: Institut für Angewandte Mathematik, Leibniz Universität Hannover, AG Wissenschaftliches Rechnen, Welfengarten 1, 30167 Hannover, Germany; and LMPS – Laboratoire de Mecanique Paris-Saclay, Université Paris-Saclay, 91190 Gif-sur-Yvette, France
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  surname: Thiele
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  organization: Institut für Angewandte Mathematik, Leibniz Universität Hannover, AG Wissenschaftliches Rechnen, Welfengarten 1, 30167 Hannover, Germany
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  givenname: Uwe
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  surname: Köcher
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  organization: Faculty of Mechanical Engineering, Helmut-Schmidt-University, University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany
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  orcidid: 0000-0002-1102-6332
  surname: Wick
  fullname: Wick, Thomas
  email: wick@ifam.uni-hannover.de
  organization: Institut für Angewandte Mathematik, Leibniz Universität Hannover, AG Wissenschaftliches Rechnen, Welfengarten 1, 30167 Hannover, Germany; and LMPS – Laboratoire de Mecanique Paris-Saclay, Université Paris-Saclay, 91190 Gif-sur-Yvette, France
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Snippet In this work, the dual-weighted residual method is applied to a space-time formulation of nonstationary Stokes and Navier–Stokes flow. Tensor-product...
In this work, the dual-weighted residual method is applied to a space-time formulation of nonstationary Stokes and Navier–Stokes flow. Tensor-product...
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StartPage 185
SubjectTerms 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
Title 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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Volume 24
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