Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization

Timo Heister, Gerd Rapin

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

Efficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. © 2012 John Wiley & Sons, Ltd.
Original languageEnglish (US)
Pages (from-to)118-134
Number of pages17
JournalInternational Journal for Numerical Methods in Fluids
Volume71
Issue number1
DOIs
StatePublished - Jan 29 2012
Externally publishedYes

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