If you want to develop numerical algorithms for variational inequalities, you often choose a Semismooth Newton Method. In many cases, this approach involves derivatives of $\max$ or $\min$ functions in respective $L^p$-spaces, which result in pointwise evaluation of functions.
However, this isn't too much of a problem, if you're discretizing with, for example, Lagrange elements, since their degrees of freedom represent pointwise evaluation in the nodes.
Your algorithm and the Newton-steps obviously can't converge, if the DOFs are integrals of the tangential components over the edges! This is the case for Nédélec Elements for $H_0(curl, \Omega)$.
I wasn't able to find anything concerning this topic, so my question: Is there literature, that works around those problems or even an easy solution?