For a 1D grid I can calculate a Lagrange polynomial through an arbitrary set of points for the reconstruction of a polynomial function.
In 2D I have an unstructured grid and want to interpolate the value on one node from the values on neighboring nodes. A difference from the 1D case is that a well-defined Lagrange polynomial has fixed stencil sizes, like 3 points for a 1st order reconstruction, 6 for a 2nd order reconstruction and so on.
What is the best approach for a reconstruction from the neighboring points? My application is a reconstruction inside a finite volumes scheme with Voronoi cells, which unlike triangles have an arbitrary (but in many meshes roughly constant) number of neighbors.