Product gauss cubature over polygons based on green's integration formula
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 N similar to mn(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.
polygons gauss-like cubature green's formula