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Calcolo

, Volume 45, Issue 3, pp 177–192 | Cite as

New bivariate polynomial expansion with boundary data on the simplex

  • Francesco Aldo Costabile
  • Francesco Dell’Accio
  • Luca Guzzardi
Article

Abstract

We introduce an extension to the two-dimensional simplex of the univariate two-point expansion formula for sufficiently smooth real functions introduced in [13]; it is a polynomial expansion with algebraic degree of exactness. This expansion is applied to obtain a new class of embedded boundary-type cubature formulae on the simplex.

Keywords

Approximation by polynomials interpolation simplex embedded cubature formulae 

Mathematics Subject Classification (2000)

Primary 41A05 41A10 65D05 65D15 Secondary 65D32 

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Copyright information

© Springer-Verlag Italia 2008

Authors and Affiliations

  • Francesco Aldo Costabile
    • 1
  • Francesco Dell’Accio
    • 1
  • Luca Guzzardi
    • 1
  1. 1.Dipartimento di MatematicaUniversità della CalabriaRende (Cs)Italy

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