How to define a test function for H^(1/2)

Dear all,
@prj @frederichecht

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 do some work to approximate H^1/2 norm

Thanks, Prof @frederichecht Sir,
And sorry for such an elementary question or for a wrong projection.

I am searching for a solution for an elliptic interface problem that includes two sub-domains:

I have to define FE space for \Omega_1, \Omega_2 and on interface \Gamma which I did like:

fespace Vh1(Th1, P1);     // for domain1 
fespace Vh2(Th2, P2);     // for domain2

Vh1 u1, v1, lambda;
Vh2 u2, v2;

for defining a weak form on interface \Gamma I have restricted the weak formulation as:

int1d(Th1, interface)( lambda * v1 )

I am not sure about it;

Kindly comment to sort out this issue.

your comments/suggestions would help me to figure out such interface boundary problems.

or, any relevant source code that can handle such interface boundary problems.

Thanks Sir