Numerische Mathematik manuscript No. (will be inserted by the editor) Higher Order Mortar Finite Element Methods in 3D with Dual Lagrange Multiplier Bases ⋆ B. P. Lamichhane 1 , R. P. Stevenson 2 , B. I. Wohlmuth 1 1 Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany, e-mail: {lamichhane,wohlmuth}@mathematik.uni-stuttgart.de 2 Department of Mathematics, Utrecht University, The Netherlands, e-mail: stevenson@math.uu.nl The date of receipt and acceptance will be inserted by the editor Summary Mortar methods with dual Lagrange multiplier bases provide a flexible, efficient and optimal way to couple different dis- cretization schemes or nonmatching triangulations. Here, we gener- alize the concept of dual Lagrange multiplier bases by relaxing the condition that the trace space of the approximation space at the slave side with zero boundary condition on the interface and the Lagrange multiplier space have the same dimension. We provide a new theo- retical framework within this relaxed setting, which opens a new and simpler way to construct dual Lagrange multiplier bases for higher order finite element spaces. As examples, we consider quadratic and cubic tetrahedral elements and quadratic serendipity hexahedral ele- ments. Numerical results illustrate the performance of our approach. Key words. Mortar finite elements, Lagrange multipliers, biorthog- onal bases, nonmatching triangulations. AMS subject classification. 35N55, 65N30. 1 Introduction Over the recent past years, mortar methods with dual Lagrange mul- tiplier bases have become an active area of research, see, e.g., [27, ⋆ This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, C12, the Netherlands Organization for Scientific Research and by the European Community’s Human Potential Programme under contract HPRN-CT- 2002-00286.