BIT Numerical Mathematics

, Volume 47, Issue 2, pp 441–453 | Cite as

Product Gauss cubature over polygons based on Green’s integration formula

  • A. Sommariva
  • M. VianelloEmail author


We have implemented in Matlab a Gauss-like cubature formula over convex, nonconvex or even multiply connected polygons. The formula is exact for polynomials of degree at most 2n-1 using Nmn 2 nodes, m being the number of sides that are not orthogonal to a given line, and not lying on it. It does not need any preprocessing like triangulation of the domain, but relies directly on univariate Gauss–Legendre quadrature via Green’s integral formula. Several numerical tests are presented.

Key words

Gauss-like cubature polygons Green’s formula 


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© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Pure and Applied MathematicsUniversity of PadovaPadovaItaly

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