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 discrete quasi-interpolants. The main problem consists in constructing the coe±cient 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 in¯nite norm. We give their explicit constructions, in¯nite norms and error estimates. We also present some numerical examples illustrating the approximation properties of the proposed quasi-interpolants