PERTURBATION OF MIXED VARIATIONAL PROBLEMS. APPLICATION TO MIXED FINITE ELEMENT METHODS.

Degrees of freedom which are Lagrange multipliers arise in the finite element approximation of mixed variational problems. When these degrees of freedom are ″local″ , the introduction of a small perturbation (corresponding by duality to a penalty function) enables the elimination of these unknowns at the element level. This method is examined for the continuous case. It is shown that the solution of the perturbed problem is close to that of the original one. This result is extended to the FEM. Several examples are given and the construction of a number of the element stiffness matrices is outlined.