Superconvergent trivariate quadratic spline quasi-interpolants on Worsey-Piper split

In this paper we use Normalized trivariate Worsey-Piper B-splines recently constructed by Sbibih et?al. (2012) and the method proposed in Sbibih et?al. (2013) to give a new representation of Worsey-Piper Hermite interpolant of any piecewise polynomial of class at least C 1 over the Worsey-Piper split in terms of its polar forms. Using this representation we construct several superconvergent discrete quasi-interpolants. The construction that we present in this work is a generalization of the one presented in Sbibih et?al. (2012) with other properties.

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