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

Type
Article

Authors
Heister, Timo
Rapin, Gerd

KAUST Grant Number
KUS-C1-016-04

Online Publication Date
2012-01-29

Print Publication Date
2013-01-10

Date
2012-01-29

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.

Citation
Heister T, Rapin G (2012) Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization. Int J Numer Meth Fluids 71: 118–134. Available: http://dx.doi.org/10.1002/fld.3654.

Acknowledgements
The majority of the research was done while both authors worked at the University of Gottingen, Germany. Timo Heister was partially supported by the German Research Foundation (DFG) through the Research Training Group GK 1023. This publication is based, in part, on the work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).

Publisher
Wiley

Journal
International Journal for Numerical Methods in Fluids

DOI
10.1002/fld.3654

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