Error Analysis of Projection Methods for Non inf-sup Stable Mixed Finite Elements: The Navier–Stokes Equations

We obtain error bounds for a modified Chorin–Teman (Euler non-incremental) method for non inf-sup stable mixed finite elements applied to the evolutionary Navier–Stokes equations. The analysis of the classical Euler non-incremental method is obtained as a particular case. We prove that the modified Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed finite elements without any kind of extra added stabilization. We show that it is also true in the case of the classical Chorin–Temam method. The relation of the methods with the so called pressure stabilized Petrov Galerkin method is established. We do not assume non-local compatibility conditions for the solution.