A mortar finite element method using dual spaces for the Lagrange multiplier

The mortar finite element method allows the coupling of different discretiz ation schemes and triangulations across subregion boundaries. In the origin al mortar approach the matching at the interface is realized by enforcing a n orthogonality relation between the jump and a modi ed trace space which s erves as a space of Lagrange multipliers. In this paper, this Lagrange mult iplier space is replaced by a dual space without losing the optimality of t he method. The advantage of this new approach is that the matching conditio n is much easier to realize. In particular, all the basis functions of the new method are supported in a few elements. The mortar map can be represent ed by a diagonal matrix; in the standard mortar method a linear system of e quations must be solved. The problem is considered in a positive definite n onconforming variational as well as an equivalent saddle-point formulation.