Improved Local Projection for the Generalized Stokes Problem (Advances in Applied Mathematics and Mechanics, 2021)
We analyze pressure stabilized finite element methods for thesolution of the generalized Stokes problem and investigate theirstability and convergence properties. An important feature of themethods is that the pressure gradient unknowns can be eliminatedlocally thus leading to a decoupled system of equations. Althoughthe stability of the method has been established, for thehomogeneous Stokes equations, the proof given here is based on theexistence of a special interpolant with additional orthogonalproperty with respect to the projection space. This makes it muchsimpler and more attractive. The resulting stabilized method isshown to lead to optimal rates of convergence for both velocity andpressure approximations.