ON PRESSURE APPROXIMATION VIA PROJECTION METHODS FOR NONSTATIONARY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

Abstract. Projection methods are an ecient tool to approximate strong solutions of the incompressible Navier-Stokes equations; as a major deciency, these methods often suer from reduced accuracy of pressure updates caused by nonphysical boundary data. After a short review, quantitative control of arising boundary layers in Chorin's scheme is given under realistic regularity assumptions. Then, we propose the new Chorin-Penalty method and verify optimal rate of convergence for pressure iterates in a general context of strong solutions. Key words. Navier-Stokes equations, incompressible uid, quasi-compressibility method, projection method. 65M12, 65M60, 65M15, 65D60, 76D05 1. Introduction. Give