Error analysis of projection methods for non inf-sup stable mixed finite elements. The Navier-Stokes equations

摘要

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