On stabilized finite element methods based on the ScottZhang projector. Circumventing the infsup condition for the Stokes problem
In this work we propose a stabilized finite element method that permits us to circumvent discrete infsup conditions, e.g. allowing equal order interpolation. The type of method we propose belongs to the family of symmetric stabilization techniques, which are based on the introduction of additional terms that penalize the difference between some quantities, i.e. the pressure gradient in the Stokes problem, and their finite element projections. The key feature of the formulation we propose is the definition of the projection to be used, a non-standard ScottZhang projector that is well-defined for L1(?) L 1 ( ? ) functions. The resulting method has some appealing features: the projector is local and nested meshes or enriched spaces are not required.
stabilized finite elements stokes problem indefinite systems