Stabilized mixed finite element methods based on Riesz-representing operators for solving saddle point problems Original Research Article

Based on Riesz-representing operators, a new stabilized finite element method is presented for saddle point problems. It is proved that this method is not subject to the discrete Babus̆ka–Brezzi condition, and that the corresponding finite element approximation problem yields a symmetrically positively definite linear system. Error bounds are obtained which are agree with the interpolation properties. As an application, the stationary Stokes problem is analyzed.