An analysis technique for stabilized finite element solution of incompressible flows

This paper presents an extension to stabilized methods of the standard tech nique for the numerical analysis of mixed methods. We prove that the stabil ity of stabilized methods follows from an underlying discrete inf-sup condi tion, plus a uniform separation property between bubble and velocity finite element spaces. We apply the technique introduced to prove the stability o f stabilized spectral element methods so as stabilized solution of the prim itive equations of the ocean.