InthispaperwegiveanoverviewofthepresentstateoffastsolversforthesolutionoftheincompressibleNavier-StokesequationsdiscretizedbythefiniteelementmethodandlinearizedbyNewtonorPicard'smethod.Itisshownthatblockpreconditionersformanexcellentapproachforthesolution,howeverifthegridsarenottofinepreconditioningwithaSaddlepointILUmatrix(SILU)maybeanattractivealternative.Theapplicabilityofallmethodstostabilizedelementsisinvestigated.Incaseofthestand-aloneStokesequationsspecialpreconditionersincreasetheefficiencyconsiderably.
