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Zbl 1199.41006
Dal\'{i}k, Josef
Optimal-order quadratic interpolation in vertices of unstructured triangulations. (English)
[J] Appl. Math., Praha 53, No. 6, 547-560 (2008). ISSN 0862-7940; ISSN 1572-9109/e

Summary: 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.

MSC 2000:: *41A05 Interpolation
41A10 Approximation by polynomials
65D05 Interpolation (numerical methods)

Keywords: interpolation of functions of two variables; strongly regular classes of triangulations; poised sets of vertices

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