Numerical integration based on bivariate quadratic spline quasi-interpolants on Powell-Sabin partitions

International audienceIn this paper we generate and study new cubature formulas based on spline quasi-interpolants in the space of quadratic Powell-Sabin splines on nonuniform triangulations of a polygonal domain in $ℝ^2$. By using a specific refinement of a generic triangulation, optimal convergence orders are obtained for some of these rules. Numerical tests are presented for illustrating the theoretical results