ON OPTIMAL FINITE-ELEMENT APPROXIMATION FOR UNILATERAL CONTACT PROBLEMS

We consider a interpolation type operator and a projection type operat or with values in a finite element function set, defined for continuou s functions and keeping positiveness. We prove with a counter-example that the two operators do not verify optimal approximation results wit h respect to a dual norm. This counter-example yields some predicted r esults concerning optimality of the mortar element method and finite e lement analysis for unilateral contact problems. (C) Academie des Scie nces/Elsevier, Paris.