Krylov improvements of the Uzawa method for Stokes type operator matrices-Reference-Cited by-同舟云学术

Krylov improvements of the Uzawa method for Stokes type operator matrices

Published:2021-07 Issue:3 Volume:148 Page:611-631
ISSN:0029-599X
Container-title:Numerische Mathematik
language:en
Short-container-title:Numer. Math.

Author:

Axelsson Owe,Karátson János

Abstract

AbstractThe paper is devoted to Krylov type modifications of the Uzawa method on the operator level for the Stokes problem in order to accelerate convergence. First block preconditioners and their effect on convergence are studied. Then it is shown that a Krylov–Uzawa iteration produces superlinear convergence on smooth domains, and estimation is given on its speed.

Funder

Eötvös Loránd University

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00211-021-01208-5.pdf

Reference32 articles.

1. Atanga, J., Silvester, D.: Iterative methods for stabilized mixed velocity-pressure finite elements. Int. J. Numer. Methods Fluids 14, 71–81 (1992)

2. Axelsson, O.: Iterative Solution Methods. Cambridge University Press, Cambridge (1994)

3. Axelsson, O.: Preconditioners for regularized saddle point matrices. J. Numer. Math. 19, 91–112 (2011)

4. Axelsson, O., Barker, V.A., Neytcheva, M., Polman, B.: Solving the Stokes problem on a massively parallel computer. Math. Model. Anal. 6, 7–27 (2001)

5. Axelsson, O., Blaheta, R., Byczanski, P., Karátson, J., Ahmad, B.: Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems. J. Comput. Appl. Math. 280, 141–157 (2015)

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Superlinear Krylov convergence under streamline diffusion FEM for convection‐dominated elliptic operators;Numerical Linear Algebra with Applications;2024-09-02

2. On the efficient preconditioning of the Stokes equations in tight geometries;Numerical Linear Algebra with Applications;2024-07-31

3. Multilevel Uzawa and Arrow–Hurwicz Algorithms for General Saddle Point Problems;Journal of Optimization Theory and Applications;2023-05-09