%0 Journal Article %1 cahouet88:IJNMF-8-869 %A Cahouet, J. %A Chabard, J. P. %D 1988 %J International Journal for Numerical Methods in Fluids %K 76m10-finite-element-methods-in-fluid-mechanics 65f08-preconditioners-for-iterative-methods 76d07-stokes-and-related-oseen-etc-flows %P 869--895 %R 10.1002/fld.1650080802 %T Some Fast 3D Finite Element Solvers for the Generalized Stokes Problem %U http://dx.doi.org/10.1002/fld.1650080802 %V 8 %X This paper is devoted to a comparison of various iterative solvers for the Stokes problem, based on the preconditioned Uzawa approach. In the first section the basic equations and general results of gradient-like methods are recalled. Then a new class of preconditioners, whose optimality will be shown, is introduced. In the last section numerical experiments and comparisons with multigrid methods prove the quality of these schemes, whose discretization is detailed.

@article{cahouet88:IJNMF-8-869, abstract = {{This paper is devoted to a comparison of various iterative solvers for the Stokes problem, based on the preconditioned Uzawa approach. In the first section the basic equations and general results of gradient-like methods are recalled. Then a new class of preconditioners, whose optimality will be shown, is introduced. In the last section numerical experiments and comparisons with multigrid methods prove the quality of these schemes, whose discretization is detailed.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Cahouet, J. and Chabard, J. P.}, biburl = {https://www.bibsonomy.org/bibtex/2e36a67373de3f9ee6dd5e62bb41651d2/gdmcbain}, citeulike-article-id = {2441059}, citeulike-attachment-1 = {cahouet_88_some_865051.pdf; /pdf/user/gdmcbain/article/2441059/865051/cahouet_88_some_865051.pdf; f705216c186777cb22c56a487589f3d668e365a1}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/fld.1650080802}, comment = {(private-note)copy provided by mshepit 2013-01-10, after I suggested it to explain the preconditioning in Fr\'{e}d\'{e}ric Hecht's Uzawa-GC.edp of late last year.}, doi = {10.1002/fld.1650080802}, file = {cahouet_88_some_865051.pdf}, interhash = {50076a2f9d18732b9b014b3ce9aeb48f}, intrahash = {e36a67373de3f9ee6dd5e62bb41651d2}, journal = {International Journal for Numerical Methods in Fluids}, keywords = {76m10-finite-element-methods-in-fluid-mechanics 65f08-preconditioners-for-iterative-methods 76d07-stokes-and-related-oseen-etc-flows}, pages = {869--895}, posted-at = {2008-02-28 10:09:58}, priority = {0}, timestamp = {2021-02-10T04:50:35.000+0100}, title = {Some Fast {3D} Finite Element Solvers for the Generalized {Stokes} Problem}, url = {http://dx.doi.org/10.1002/fld.1650080802}, volume = 8, year = 1988 }