  A priori analysis for a generalized local projection stabilized conforming
finite element approximation of Darcy flow and Stokes problems is presented in
this paper. A first-order conforming P1 finite element space is used to
approximate both the velocity and the pressure. It is shown that the stabilized
discrete bilinear form satisfy the inf-sup condition with respect to a
generalized local projection norm. Moreover, a priori error estimates are
derived for both problems. Finally, the validation of the proposed
stabilization scheme is demonstrated with appropriate numerical examples.
