الملخص الإنجليزي
Numerical approximation of incompressible flows presents a major difficulty, namely, the need to satisfy a compatibility condition between the discrete velocity and pressure spaces. This condition which has been well known since the work of Babuska and Brezzi in the seventies prevents, in particular, the use of equal order interpolation spaces for the two variables, which is the most attractive choice from a computational point of view.
To overcome this difficulty, residual based stabilized finite element methods that circumvent the restrictive inf-sup condition have been developed for Stokes-like problem. These methods, though having optimal rates of convergence, their performance depends on the choice of local parameters. To relax the strong coupling between the velocity and the pressure, local projection methods that are less sensitive to the choice of parameters have been proposed.
In this thesis, the convergence and stability of local projection methods have been investigated and enriched equal order finite element velocity-pressure approximations are introduced. Numerical examples will be presented to validate the analysis.
