Perturbation of mixed variational problems. Application to mixed finite element methods

Degrees of freedom which are Lagrange multipliers anse in the finite element approximation of mixed vanational problems. When these degrees of freedom are "local", the intioduction of a small perturbation {conespondinq hv duality to a penalty function) enables the élimination of these unknouns at the element level We fitst examine this method in the continuons case and show that the solution of the perturbed problem is close to that oj the original one. We extend this result to the FEM Several examples are gwen and the construction of a number of the element stiffness matrices is outhned