Local projection stabilization for incompressible flows: Equal-order vs. inf-sup stable interpolation

Abstract

A standard approach to the non-stationary, incompressible Navier-Stokes model is to split the problem into linearized auxiliary problems of Oseen type. In this paper, a unified numerical analysis for finite element discretizations using the local projection stabilization method with either equal-order or inf-sup stable velocity-pressure pairs in the case of continuous pressure approximation is presented. Moreover, a careful comparison of both variants is given.