Generalized local projection stabilized nonconforming finite element methods for Darcy equations

An a priori analysis for a generalized local projection stabilized finite element solution of the Darcy equations is presented in this paper. A first-order nonconforming P nc 1 finite element space is used to approximate the velocity, whereas the pressure is approximated using two different finite elements, namely piecewise constant P0 and piecewise linear nonconforming P nc 1 elements. The considered finite element pairs, P nc 1 /P0 and P nc 1 /P nc 1 , are inconsistent and incompatibility, respectively, for the Darcy problem. The stabilized discrete bilinear form satisfies an inf-sup condition with a generalized local projection norm. Moreover, a priori error estimates are established for both finite element pairs. Finally, the validation of the proposed stabilization scheme is demonstrated with appropriate numerical examples