ABSTRACT
Mixed finite element methods differ from standard finite element schemes in their use of stationary variational principles, i.e., principles which characterize the solution of the problem to be approximated as a stationary point rather than as a strict minimum or maximum. One consequence of this property is the possibility of instabilities in the approximation. From a practical standpoint it is important that these conditions be as sharp as possible so that the user not be forced into needless complications to obtain stable and accurate approximations. This chapter studies the implications for the structure of the errors made in mixed finite element formulations by giving an equivalent formulation of Brezzi’s theory in terms of inclusion and decomposition properties. Concrete examples are used to illustrate the general setting of the equivalent formulation of Brezzi’s theory.
