Role of the LBB condition in weak spectral projection methods

This paper investigates the relevance of the Ladyshenskaya-Babuska-Brezzi condition in spectral projection methods. We consider the stability and convergence properties for a first-order nonincremental projection method and a second-order incremental projection method, both based on a spectral Galerkin-Leggendre spatial discretization. We show that the convergence of both projection methods is controlled by the ability of the spectral framework to approximate correctly the steady Stokes problem. (C) 2001 Elsevier Science.