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


Timo Heister, Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA.



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.