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Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization
Author(s) -
Heister Timo,
Rapin Gerd
Publication year - 2012
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.3654
Subject(s) - preconditioner , discretization , augmented lagrangian method , schur complement , mathematics , type (biology) , lagrangian , finite element method , algebraic number , mathematical optimization , iterative method , mathematical analysis , physics , ecology , eigenvalues and eigenvectors , quantum mechanics , biology , thermodynamics
SUMMARY 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. Copyright © 2012 John Wiley & Sons, Ltd.