Abstract
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.
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