Mixed finite element approximation for a contact problem in electro-elasticity
Keywords:
Adhesion, electro-elastic materials, error estimates, frictionless contact, mixed formulation.Abstract
The present paper is concerned with the frictionless contact problem between two electroelasticbodies in a bidimensional context. We consider a mixed formulation in which theunknowns are the displacement field, the electric potential field and the contact pressure. Weuse the mixed finite element method to approximate the solutions. Error estimates are derivedon the approximative solutions from which the convergence of the algorithm is deduced undersuitable regularity conditions on the exact solution.References
Batra, R. C. & Yang, J. S. 1995. Saint-Venant’s principle in linear piezoelectricity.
Journal of Elasticity 38: 209-218.
Bisenga, P., Lebon, F. & Maceri, F. 2002. The unilateral frictional contact of a
piezoelectric body with a rigid support, in Contact Mechanics, J.A.C. Martins
and Manuel D.P. Monteiro Marques (Eds.). Kluwer, Dordrecht: 347-354.
Ciarlet, P. G. 1991. The finite element method for elliptic problems, In Handbook
of Numerical Analysis, Volume II,Part1, Eds.P.G.Ciarlet and J.L.Lions. North
Holland Publishing, Amsterdam.
Coorevits, P. Hild, P. Lahalouani, K. & Sassi, T. 2002. Mixed finite element
methods for unilateral contact problems: convergence analysis and numerical
studies. Mathematics of Computation 71(237): 1–25.
Crouzeix, M. & Thome, V. 1987. The stability in LP and W1, p of the L2 -projection
on finite element function spaces. Mathematics of computation 48: 521-532.
Haslinger, J., Hlavác