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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

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  • $\begingroup$ InterpolationOrder -> 2 (?) $\endgroup$
    – Xminer
    Commented May 31, 2019 at 1:22

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InterpolatingFunction based on triangular unstructured grid uses Lagrange interpolation. Same method is used if InterpolatingFunction is created from predefined ElementMesh object (with "MeshOrder" 1 or 2) by using ElementMeshInterpolation[{mesh}, values].

For interpolation on regular grids of points you can choose between Method->"Hermite" or Method->"Spline" of arbitrary order. Method "Spline" gives you continuous derivatives.

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