Construction of 2D explicit cubic quasi-interpolating splines in Bernstein-B\'ezier form
Abstract
In this paper, the construction of C1 cubic quasi-interpolants on a three-direction mesh of 2 is addressed. The quasi-interpolating splines are defined by directly setting their Bernstein-B\'ezier coefficients relative to each triangle from point and gradient values in order to reproduce the polynomials of the highest possible degree. Moreover, additional global properties are required. Finally, we provide some numerical tests confirming the approximation properties.
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