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J. Melenk, B. Wohlmuth:
"Quasi-optimal approximation of surface based Lagrange multipliers in finite element methods";
in: "ASC Report 13/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

We show quasi-optimal a priori convergence results in the L2- and H−1/2-norm for
the approximation of surface based Lagrange multipliers such as those employed in the mortar finite
element method. We improve on the estimates obtained in the standard saddle point theory, where
error estimates for both the primal and dual variables are obtained simultaneously and thus only
suboptimal a priori estimates for the dual variable are reached. We illustrate that an additional
factor ph| ln h| in the a priori bound for the dual variable can be recovered by using new estimates
for the primal variable in strips of width O(h) near these surfaces.

http://www.asc.tuwien.ac.at/preprint/2011/asc13x2011.pdf