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

摘要

Projection methods are an efficient tool to approximate strong solutions of the incompressible Navier–Stokes equations. As a major deficiency, these methods often suffer from reduced accuracy for pressure iterates caused by nonphysical boundary data, going along with suboptimal error estimates for pressure iterates. We verify a rigorous bound for arising boundary layers in Chorin’s scheme under realistic regularity assumptions. In a second step, the new Chorin–Penalty method is proposed, where optimal rate of convergence for pressure iterates is shown.