%0 Journal Article %1 heister2013efficient %A Heister, Timo %A Rapin, Gerd %D 2013 %J International Journal for Numerical Methods in Fluids %K 65n22-pdes-bvps-solution-of-discretized-equations 65n30-pdes-bvps-finite-elements 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics %N 1 %P 118-134 %R 10.1002/fld.3654 %T Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization %U https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.3654 %V 71 %X 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.

@article{heister2013efficient, 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. }, added-at = {2020-06-24T08:23:48.000+0200}, author = {Heister, Timo and Rapin, Gerd}, biburl = {https://www.bibsonomy.org/bibtex/268805e6a9eece0906db9bb72ccc19425/gdmcbain}, doi = {10.1002/fld.3654}, interhash = {e85e4a2a502032bb84efa4b6d6599088}, intrahash = {68805e6a9eece0906db9bb72ccc19425}, journal = {International Journal for Numerical Methods in Fluids}, keywords = {65n22-pdes-bvps-solution-of-discretized-equations 65n30-pdes-bvps-finite-elements 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics}, number = 1, pages = {118-134}, timestamp = {2020-06-24T08:23:48.000+0200}, title = {Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.3654}, volume = 71, year = 2013 }