Abstract
In this paper, we use the finite element method to construct a new normalized basis of a univariate C2 cubic spline space endowed with a specific subdivision of a real interval. Based on the polar forms, we introduce a new representation of the Hermite interpolant of any C2 piecewise polynomial defined over this subdivision and we construct several superconvergent discrete quasi-interpolants which have an optimal approximation order. This approach is simple and provides an interesting approximation. Numerical results are given to illustrate the theoretical ones.
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