Abstract
In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness r and total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].
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Dong, H. A new formulation of Bernstein-Bezier based smoothness conditions forpp functions. Approx. Theory & its Appl. 11, 67–75 (1995). https://doi.org/10.1007/BF02836280
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DOI: https://doi.org/10.1007/BF02836280