Quasi-Optimal Approximation of Surface Based Lagrange Multipliers in Finite Element Methods

We show quasi-optimal a priori convergence results in the Land 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 √ h| lnh| 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. AMS subject classification: 65N30