Role of the LBB Condition in Weak Spectral Projection Methods

This paper investigates the relevance of the Ladyshenskaya–Babuška–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–Legendre 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.