What is the logic behind the parameter TwoPunctures::Newton_maxit?  Its default is set to 5, and if the Newton iteration doesn't converge in this number of iterations, the solution is just used anyway.  Shouldn't there be a fatal error in this case?  Is it ever legitimate to use a solution which has not converged to within the tolerance?  I think I would prefer to be told to specify a larger tolerance than to have a solution which does not meet the tolerance I set.