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

摘要

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 Babugka-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.