I am trying to use 
NDSolve\`FEM\`ElementMeshInterpolation
on a triangular structured grid constructed from a Delaunay triangulation with zero area triangles dropped.
My question is regarding the kind of spline interpolation being used--I would like at least C^1 accuracy, but none of the options shown seem to have any effect. 

>  {  {"ExtrapolationHandler" -> Automatic},  {InterpolationOrder ->
> Automatic},  {Method -> Automatic},  {PeriodicInterpolation -> False}
> }

Anyone who knows how this works or where this is documented?
Niels