Nitsche's method for interface problems

Interfaces between domains with differing material properties require aligned 
meshes in order to give optimal convergence rates in finite element 
discretization methods. Examples of such interface problems are inclusions, 
melt fronts, or cracks. In this talk, I will consider the possibility of 
letting the interface run through the physical elements, avoiding mesh 
alignment, and use the Nitsche (AKA discontinuous Galerkin) method to ensure 
continuity in temperature and/or flux (displacements and/or stress). 
Applications will be given to Poisson's equation and small strain elastic 
inclusion and crack problems. I will also present, using a similar concept, 
stable overlapping mesh methods of arbitrary order of accuracy, methods which 
retain underlying symmetries of the continuous problem if they are present.