ANALYSIS OF THE CONVERGENCE OF MIXED FINITE ELEMENT METHODS.

Abstract

Convergence proofs in mixed finite element methods are considered. After referring to abstract conditions of F. Brezzi, it is shown that these conditions are, in some cases, equivalent to the possibility of building a uniformly continuous operator PI //h from V to V//h. Some properties of discrete operators involved in the approximation are characterized. Two examples show that building the operator PI //h can be done through an interpolation operator. A third example presents a case which is still out of reach of present techniques.