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Local quadratic interpolation in vertices of regular triangulations. (English) Zbl 1217.41005
Summary: This paper is devoted to the problem of Lagrange interpolation of functions in two variables by quadratic polynomials under the restriction that the nodes of interpolation are vertices of a triangulation. We prove that every pair of an inner vertex and its neighbour in a regular triangulation without obtuse angles belongs to a local six-tuple $$c^1,\dots,c^6$$ of vertices such that there always exists a unique quadratic interpolation polynomial in the nodes $$c^1,\dots,c^6$$.

##### MSC:
 41A05 Interpolation in approximation theory 41A10 Approximation by polynomials 65D05 Numerical interpolation