Error analysis of fully discrete velocity-correction methods for incompressible flows

Abstract

A fully discrete version of the velocity-correction method, proposed by Guermond and Shen (2003) for the time-dependent Navier-Stokes equations, is introduced and analyzed. It is shown that, when accounting for space discretization, additional consistency terms, which vanish when space is not discretized, have to be added to establish stability and optimal convergence. Error estimates are derived for both the standard version and the rotational version of the method. These error estimates are consistent with those by Guermond and Shen (2003) as far as time discretiztion is concerned and are optimal in space for finite elements satisfying the inf-sup condition. ©2008 American Mathematical Society.