Cubature rule associated with a discrete blending sum of quadratic spline quasi-interpolants

Authors:
Vittoria Demichelis;Paul Sablonnière
Affiliations:
Dipartimento di Matematica, Universití di Torino, via Carlo Alberto 10, 10123 Torino, Italy;Centre de Mathématiques, INSA de Rennes, 20 Avenue des Buttes de Coësmes, CS 14315, 35043 Rennes Cedex, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 2
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Abstract

A new cubature rule for a parallelepiped domain is defined by integrating a discrete blending sum of C^1 quadratic spline quasi-interpolants in one and two variables. We give the weights and the nodes of this cubature rule and we study the associated error estimates for smooth functions. We compare our method with cubature rules based on the tensor products of spline quadratures and classical composite Simpson's rules.