Mixed formulations for a class of variational inequalities
Université de Moncton,
Campus de Shippagen, 218, boulevard J.-D. Gauthier, Shippagen,
Nouveau Brunswick, E831P6, Canada.
2 Laboratoire MIP, UMR-CNRS 5640, INSA de Toulouse, 135 Avenue de Rangueil, 31077, Toulouse Cedex 4, France. email@example.com.
3 Laboratoire MIP, UMR-CNRS 5640, Université Toulouse 3, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France. firstname.lastname@example.org.
A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed finite element method of Raviart–Thomas is proved to converge with a quasi-optimal error bound.
Mathematics Subject Classification: 35J85 / 76M30
Key words: Variational inequalities / unilateral problems / Signorini problem / contact problems / mixed finite element methods / elliptic PDE.
© EDP Sciences, SMAI, 2004