Geodesic
Optimal-order quadratic interpolation in vertices of unstructured triangulations
Applications of Mathematics, Tome 53 (2008) no. 6, pp. 547-560.

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We study the problem of Lagrange interpolation of functions of two variables by quadratic polynomials under the condition that nodes of interpolation are vertices of a triangulation. For an extensive class of triangulations we prove that every inner vertex belongs to a local six-tuple of vertices which, used as nodes of interpolation, have the following property: For every smooth function there exists a unique quadratic Lagrange interpolation polynomial and the related local interpolation error is of optimal order. The existence of such six-tuples of vertices is a precondition for a successful application of certain post-processing procedures to the finite-element approximations of the solutions of differential problems.
DOI : 10.1007/s10492-008-0041-x
Classification : 41A05, 41A10, 41A63, 65D05
Keywords: interpolation of functions of two variables; strongly regular classes of triangulations; poised sets of vertices 
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Dalík, Josef. Optimal-order quadratic interpolation in vertices of unstructured triangulations. Applications of Mathematics, Tome 53 (2008) no. 6, pp. 547-560. doi : 10.1007/s10492-008-0041-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0041-x/

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