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Block preconditioners for finite element discretization of incompressible flow with thermal convection
Author(s) -
Howle Victoria E.,
Kirby Robert C.
Publication year - 2012
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1814
Subject(s) - mathematics , discretization , finite element method , block (permutation group theory) , compressibility , incompressible flow , mixed finite element method , flow (mathematics) , convection , mechanics , mathematical analysis , geometry , thermodynamics , physics
SUMMARY We derive block preconditioners for a finite element discretization of incompressible flow coupled to heat transport by the Boussinesq approximation. Our techniques rely on effectively approximating the Schur complement obtained by eliminating the fluid variables to obtain an equation for temperature alone. Additionally, the method utilizes existing block‐structured preconditioners and multilevel methods for the Navier–Stokes equations and scalar convection–diffusion. We find that the preconditioner remains robust and scalable even when the subsolves are applied quite inexactly. Copyright © 2012 John Wiley & Sons, Ltd.