Error bounds on the approximation of functions and partial derivatives by quadratic spline quasi-interpolants on non-uniform criss-cross triangulations of a rectangular domain

Dagnino Catterina (1) , Sara Remogna (1) , Paul Sablonnière (2)

1 Dipartimento di Matematica
2 IRMAR - Institut de Recherche Mathématique de Rennes

Given a non-uniform criss-cross triangulation of a rectangular domain $\Omega$, we consider the approximation of a function f and its partial derivatives, by general $C^1$ quadratic spline quasi-interpolants and their derivatives. We give error bounds in terms of the smoothness of f and the characteristics of the triangulation. Then, the preceding theoretical results are compared with similar results in the literature. Finally, several examples are proposed for illustrating various applications of the quasi-interpolants studied in the paper.

Mots clés: Bivariate splines; Quasi-interpolation; Derivative approximation

Domaines: Analyse numérique [math.NA]

Dagnino Catterina, Sara Remogna, Paul Sablonnière. Error bounds on the approximation of functions and partial derivatives by quadratic spline quasi-interpolants on non-uniform criss-cross triangulations of a rectangular domain. BIT Numerical Mathematics, 2013, 53 (1), pp.87-109. ⟨10.1007/s10543-012-0392-2⟩. ⟨hal-00847651⟩