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On iterative methods for the incompressible Stokes problem
Author(s) -
ur Rehman M.,
Geenen T.,
Vuik C.,
Segal G.,
MacLachlan S. P.
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2235
Subject(s) - schur complement , preconditioner , mathematics , discretization , complement (music) , matrix (chemical analysis) , mass matrix , mathematical analysis , compressibility , convergence (economics) , iterative method , constant (computer programming) , linear system , mathematical optimization , physics , computer science , eigenvalues and eigenvectors , materials science , economic growth , chemistry , composite material , biochemistry , quantum mechanics , nuclear physics , thermodynamics , complementation , neutrino , economics , gene , phenotype , programming language
In this paper, we discuss various techniques for solving the system of linear equations that arise from the discretization of the incompressible Stokes equations by the finite‐element method. The proposed solution methods, based on a suitable approximation of the Schur‐complement matrix, are shown to be very effective for a variety of problems. In this paper, we discuss three types of iterative methods. Two of these approaches use the pressure mass matrix as preconditioner (or an approximation) to the Schur complement, whereas the third uses an approximation based on the ideas of least‐squares commutators (LSC). We observe that the approximation based on the pressure mass matrix gives h‐independent convergence, for both constant and variable viscosity. Copyright © 2010 John Wiley & Sons, Ltd.