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

Paul Sablonnière (1) , Driss Sbibih (2) , M. Tahrichi (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Laboratoire MATSI

In 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.

Mots clés: Cubature rule; Spline quasi-interpolant; Powell-Sabin spline

Domaines: Analyse numérique [math.NA]

Paul Sablonnière, Driss Sbibih, M. Tahrichi. Numerical integration based on bivariate quadratic spline quasi-interpolants on Powell-Sabin partitions. BIT Numerical Mathematics, 2013, 53 (1), pp.175-192. ⟨10.1007/s10543-012-0391-3⟩. ⟨hal-00847713⟩