Running some test cases pointed out that the extrapolation from first order Lagrange basis functions to those higher than third order cubic Lagrange basis functions were in error. The extrapolated functions had high degrees of oscillations. The bug has been reported to the developers. They have put in a check so that the first release will throw an error instead of attempting an extrapolation.
So it's back to traditional interpolation methods. Keep this in mind when viewing the code from the last two posts.