Details
| Original language | English |
|---|---|
| Pages (from-to) | A1599-A1627 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 46 |
| Issue number | 3 |
| Early online date | 9 May 2024 |
| Publication status | Published - 2024 |
Abstract
We consider the widely used continuous \scrQk-\scrQk-1 quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Schöberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.
Keywords
- matrix-free implementation, mixed finite element discretization, multigrid methods, Stokes and generalized Stokes problems
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Scientific Computing, Vol. 46, No. 3, 2024, p. A1599-A1627.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Matrix-Free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems
AU - Jodlbauer, Daniel
AU - Langer, Ulrich
AU - Wick, Thomas
AU - Zulehner, Walter
N1 - Publisher Copyright: Copyright © by SIAM.
PY - 2024
Y1 - 2024
N2 - We consider the widely used continuous \scrQk-\scrQk-1 quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Schöberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.
AB - We consider the widely used continuous \scrQk-\scrQk-1 quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Schöberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.
KW - matrix-free implementation
KW - mixed finite element discretization
KW - multigrid methods
KW - Stokes and generalized Stokes problems
UR - http://www.scopus.com/inward/record.url?scp=85194353041&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2205.15770
DO - 10.48550/arXiv.2205.15770
M3 - Article
AN - SCOPUS:85194353041
VL - 46
SP - A1599-A1627
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
SN - 1064-8275
IS - 3
ER -