I am working with finite elements using domain decomposition in 2D and one of the solutions I need to obtain is the co-normal derivative of the solution along a segment that is the intersection of two subdomains.
From trace theorems and Sobolev spaces, it is known that this derivative is in $H^{-1/2}$, and therefore convergence is also proven in that space. My question is: once I have obtained my discrete FEM solution for this derivative, how can compute its $H^{-1/2}$ norm?
Since it is defined as the dual space of $H^{1/2}$, I have not found any way of effectively computing the $H^{-1/2}$ norm of a function.
Someone mentioned to me that the use of wavelets could be a possible way but I haven't found any resource backing up that claim. I appreciate the help, thanks in advance.