Stable Lagrange multipliers for quadrilateral meshes of curved interfaces in 3D

For the discretization of coupled problems by means of mortar finite elements, the choice of the discrete Lagrange multiplier space is of crucial importance for the performance of the resulting numerical scheme. Dual Lagrange multipliers offer several advantages since they can be locally eliminated. In this paper, the lowest order dual Lagrange multipliers are extended to arbitrary quadrilateral or triangular surface grids. In a first step, two alternatives are provided for the case of planar interfaces. For the approximation of vector fields, two more modifications are given for use on curvilinear interfaces. A priori results are obtained and several numerical examples are shown.