On trivariate blending sums of univariate and bivariate quadratic spline quasi-interpolants on bounded domains

The aim of this paper is to investigate, in a bounded domain of R³, two blending sums of univariate and bivariate C¹ quadratic spline quasi-interpolants.The main problem consists in constructing the coefficient functionals associated with boundary generators, i.e. generators with supports not entirely inside the domain. In their definition, these functionals involve data points lying inside or on the boundary of the domain. Moreover, the weights of these functionals must be chosen so that the quasi-interpolants have the best approximation order and a reasonable infinite norm.We give their explicit constructions, infinite norms and error estimates. In order to illustrate the approximation properties of the proposed quasi-interpolants, some numerical examples are presented and compared with those obtained by some other trivariate quasi-interpolants given recently in the literature.