Finite element approximations of the stokes flow problem based upon various variational principles

Finite element methods are constructed by adding to the usual Galerkin method terms that are mesh-dependent least-squares forms of the Euler-Lagrange equations. The methods are consistent and possess additional stability compared to the Galerkin method. Finite element interpolations, which are unstable in the Galerkin approach, are now convergent. The methodology is applied to the velocity-pressure formulation, a.k.a., Herrmann's formulation, to the stress-velocity formulation, a.k.a., Hellinger-Reissner's formulation and to a new formulation based on augmented stress, pressure and velocity