On optimal finite element approximation for unilateral contact problems. (À propros d’approximation par éléments finis optimale pour les problèmes de contact unilatéral.) (French) Zbl 0914.73060
Summary: We consider an interpolation-type operator and a projection-type operator with values in a finite element function set, defined for continuous functions and keeping positiveness. We prove with a counter-example that the two operators do not provide optimal approximation in the dual norm. This counter-example yields also some results concerning optimality of the mortar element method and finite element analysis for unilateral contact problems.
MSC:
74S05 | Finite element methods applied to problems in solid mechanics |
74A55 | Theories of friction (tribology) |
74M15 | Contact in solid mechanics |