On Polynomial Reproduction of Dual FE Bases

We construct local piecewise polynomial dual bases for standard Lagrange finite element spaces which themselves provide maximal polynomial reproduction. This answers a question which came up in connection with the second author's research on mortar finite elements. By means of such dual bases for the lagrange multiplier, extremely efficient realization of mortar methods on non-matching triangulations can be obtained without losing the optimality of the discretization errors. In contrast to the standard mortar approach, the locality of the basis functions is preserved.