Towards an Implementation of Nitsche's Method on Overlapping Meshes in 3D

Nitsche's method may be used to derive a systematic finite element formulation for problems with overlapping meshes that is stable and has optimal order. In this note, we formulate the method for a linear elastic model problem with discontinuous material properties. We discuss the implementation aspects, including computation of intersections of elements and integrals on the resulting polyhedra, and illustrate the method on a three dimensional test problem