Details
| Original language | English |
|---|---|
| Pages (from-to) | 185-214 |
| Number of pages | 30 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 24 |
| Issue number | 1 |
| Early online date | 31 May 2023 |
| Publication status | Published - 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
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational Methods in Applied Mathematics, Vol. 24, No. 1, 01.01.2024, p. 185-214.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Tensor-Product Space-Time Goal-Oriented Error Control and Adaptivity with Partition-of-Unity Dual-Weighted Residuals for Nonstationary Flow Problems
AU - Roth, Julian
AU - Thiele, Jan Philipp
AU - Köcher, Uwe
AU - Wick, Thomas
N1 - Funding Information: The first and fourth authors acknowledge the funding of the German Research Foundation (DFG; http://dx.doi.org/10.13039/501100001659) within the framework of the International Research Training Group on Computational Mechanics Techniques in High Dimensions GRK 2657 under Grant Number 433082294.
PY - 2024/1/1
Y1 - 2024/1/1
N2 - 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.
AB - 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.
KW - Dual-Weighted Residuals
KW - Dynamically Changing Meshes
KW - Incompressible Navier-Stokes Equations
KW - Mesh Adaptivity
KW - Tensor-Product Space-Time Finite Elements
UR - http://www.scopus.com/inward/record.url?scp=85160852852&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2210.02965
DO - 10.48550/arXiv.2210.02965
M3 - Article
AN - SCOPUS:85160852852
VL - 24
SP - 185
EP - 214
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
SN - 1609-4840
IS - 1
ER -