I know the values for a function v[x,y] on an irregular grid of (x,y) points. Call the table storing all these points xyvtriples. Because of the irregular grid, the Mathematica function Interpolation only works as
interpolatedvfunc = Interpolation[xyvtriples, InterpolationOrder -> 1];
But what I really need are the partial derivatives of interpolatedfunc with respect to each argument, and for those partials to be continuous, which won't happen due to the edges produced by InterpolatioOrder -> 1.
Is there any way around this? I can make a very fine grid of (x,y) points to (I hope) counter any problems with forcing a spline like interpolation if I can somehow force this to happen.
Thanks.
NDSolve
can do it, you can, too: (E.g.usol = NDSolve[{-Laplacian[u[x, y], {x, y}] == 1, DirichletCondition[u[x, y] == 0, True]}, u, {x, y} \[Element] Disk[]]; Plot3D[Evaluate[D[u[x, y], x] /. First[usol]], {x, y} \[Element] Disk[]]
. But I don't understand your setup/workflow and feel it's not worth trying something out I don't really need and don't know if it will help. Please give a minimal working example (in code) for us to copy/paste and play with. $\endgroup$Interpolation
will accept it at higher order? $\endgroup$polyharmonicSpline[]
. $\endgroup$