Construction of a normalized basis of a univariate quadratic $C^1$ spline space and application to the quasi-interpolation
Resumen
In this paper, we use the finite element method to construct a new normalized basis of a univariate quadratic $C^1$ spline space. We give a new representation of Hermite interpolant of any piecewise polynomial of class at least $C^1$ in terms of its polar form. We use this representation for constructing several superconvergent and super-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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