Design of a Stable Lagrange Multiplier Space for Stiff Boundary Conditions

We introduce a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the eXtended Finite Element Method. In contrast to earlier approaches, we do not work with an interior penalty formulation as, e.g., for Nitsche techniques, but impose the constraints weakly in terms of Lagrange multipliers. The new algorithm allows a local construction of the Lagrange multiplier space while improving the accuracy of the computed fields. The originality of this approach with regard to former approaches lies in the use of the trace of primary shape functions defined on the domain, and a simplified procedure to define the mesh on the interface. Moreover, the newly constructed Lagrange multiplier space satisfies, in contrast to the naive approach, a uniform inf-sup condition.