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

Abstract

We obtain error bounds for a modi ed Chorin-Teman (Euler non- incremental) method for non inf-sup stable mixed nite elements ap- plied to the evolutionary Navier-Stokes equations. The analysis of the classical Euler non-incremental method is obtained as a particu- lar case. We prove that the modi ed Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed nite 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 sta- bilized Petrov Galerkin method (PSPG) is established. We do not assume non-local compatibility conditions for the solution.