Error analysis of projection methods for non inf-sup stable mixed finite elements. The Navier-Stokes equations
Provides theoretical justification for using simpler finite element pairs in Navier-Stokes simulations, but the contribution is incremental as it extends existing analysis.
The paper derives error bounds for a modified Chorin-Teman method that allows the use of non inf-sup stable mixed finite elements for the Navier-Stokes equations without extra stabilization, and shows the classical method also has this property. No concrete numerical results are provided.
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 (PSPG) is established. We do not assume non-local compatibility conditions for the solution.