How to define a test space (trace space) H^(1/2) over an interface of two sub-domains?
or, the only restriction of a test space that is defined for a sub-domain over the interface will work in this case (like in the Schwarz non-overlapping scheme)
This question prove that you do not understand Finite element method.
Sorry, no answers but Eliseo Chacon Vera eliseo@um.es do some work to approximate H^1/2 norm