Role of the LBB Condition in Weak Spectral Projection Methods

✍ Scribed by F. Auteri; J.-L. Guermond; N. Parolini

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 424 KB
• Volume: 174
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.2001.6922

✦ Synopsis

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.