Least Squares Preconditioners for Stabilized Discretizations of the Navier-Stokes Equations

Authors:
Howard Elman;Victoria E. Howle;John Shadid;David Silvester;Ray Tuminaro
Affiliations:
-;-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2007

Citing 0
Cited 4

A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations

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A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations

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Stabilization and scalable block preconditioning for the Navier-Stokes equations

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Analysis of Augmented Lagrangian-Based Preconditioners for the Steady Incompressible Navier-Stokes Equations

SIAM Journal on Scientific Computing

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Abstract

This paper introduces two stabilization schemes for the least squares commutator (LSC) preconditioner developed by Elman, Howle, Shadid, Shuttleworth, and Tuminaro [SIAM J. Sci. Comput., 27 (2006), pp. 1651-1668] for the incompressible Navier-Stokes equations. This preconditioning methodology is one of several choices that are effective for Navier-Stokes equations, and it has the advantage of being defined from strictly algebraic considerations. It has previously been limited in its applicability to div-stable discretizations of the Navier-Stokes equations. This paper shows how to extend the same methodology to stabilized low-order mixed finite element approximation methods.