Remarks on projection methods for the approximation of Navier-Stokes equations. (Remarques sur les méthodes de projection pour l’approximation des équations de Navier-Stokes.) (French) Zbl 0802.76057

Guermond, Jean-Luc

Numer. Math. 67, No. 4, 465-473 (1994).

This paper shows that the convergence estimates on the pressure for projection methods presented in [J. Shen, SIAM J. Numer. Anal. 29, No. 1, 57-77 (1992; Zbl 0741.76051), and Numer. Math. 62, No. 1, 49-74 (1992; Zbl 0739.76017)] are not correctly obtained since they are based on an inequality which is not correct. A counter-example is given. As conclusion, the conjecture that projection methods yield convergence rates of order higher than \(O(\delta t^{1/2})\) for the pressure remains an open question.

Reviewer: J.-L.Guermond

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

counter-example; convergence rates

Citations:

Zbl 0741.76051; Zbl 0739.76017