TY - JOUR
T1 - Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization
AU - Heister, Timo
AU - Rapin, Gerd
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2012/1/29
Y1 - 2012/1/29
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/598100
UR - http://doi.wiley.com/10.1002/fld.3654
UR - http://www.scopus.com/inward/record.url?scp=84872395147&partnerID=8YFLogxK
U2 - 10.1002/fld.3654
DO - 10.1002/fld.3654
M3 - Article
SN - 0271-2091
VL - 71
SP - 118
EP - 134
JO - International Journal for Numerical Methods in Fluids
JF - International Journal for Numerical Methods in Fluids
IS - 1
ER -