Error Bounds for Hermite Interpolation by Quadratic Splines on an -Triangulation

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Abstract
For α ≥ l, an α-triangulation Fα of a planar domain is such that, for every T ∈ Fα, there holds 1 ≤ RT/2rT ≤ α, where RT (resp. rT) denotes the radius of the circumscribed (resp. inscribed) circle of the triangle T. When T is varying in Fα the centre of its inscribed circle is varying in a compact interior to T and its orthogonal projections on the sides are varying in compact intervals interior to these sides. Precise results are given about the sizes of these compacts and are used for the computation of error constants in the problem of Hermite interpolation by Powell-Sabin quadratic finite elements, bringing to the fore their dependence on the parameter α.

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