The Dual Mixed Method for an Unilateral Problem

Abstract

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqueness of the solution of the problem are presented, and error bounds $O(h^{\frac{3}{4}})$ and $O(h^{\frac{3}{2}})$ are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for $k=0$ and $k=1$ respectively.