On Symmetric Cubature Formulae for Planar Regions
J. I. Maeztu · IMA Journal of Numerical Analysis · 1989
This paper is concerned with , Dm-symmetric, cubature formulae for Dm-symmetric planar regions of integration, Dm being the dihedral group of order 2m, that is, the symmetry group of a regular polygon with m edges. A unified theory for the analysis of this kind of formula set is introduced. This theory arises from the identification of the space of all polynomials that are invariant with respect to the symmetry group Dm. The type of analysis used leads to a simple method for constructing this kind of cubature formula set, even when a high degree of polynomial precision is required.