Role of the LBB condition in weak spectral projection methods

This paper investigates the relevance of the Ladyshenskaya-Babuska-Brezzi c ondition in spectral projection methods. We consider the stability and conv ergence properties for a first-order nonincremental projection method and a second-order incremental projection method, both based on a spectral Galer kin-Leggendre spatial discretization. We show that the convergence of both projection methods is controlled by the ability of the spectral framework t o approximate correctly the steady Stokes problem. (C) 2001 Elsevier Scienc e.