Domain Decomposition and fem variables

In the example about Domain Decomposition, for the “Schwarz non overlapping Scheme”, lambda is actualized as: lambda = lambda - (u-U)/2

What I don’t really understand is that U is a fem variable defined inside a mostly circular domain cut by a inclined line, and u is a fem variable defined inside rectangular domain with an inclined side that coincides with that one of the circular domain.

So, what does U-u mean? Those variables are defined over different domains that have a common boundary. So, in general, what do operate mixing variables of different domains mean?


This depend strongly of the definition of lambda, here lambda is defined on the intersection of the two domain so no problem.