Lai, Ming-Jun Approximation order for bivariate \(C^ 1\)-cubics on a four-directional mesh is full. (English) Zbl 0792.41023 Comput. Aided Geom. Des. 11, No. 2, 215-223 (1994). Summary: We show that the space of bivariate \(C^ 1\) piecewise cubic polynomial functions on a four-directional mesh of size \(h\) has the full approximation order, i.e., \(O(h^ 4)\). Cited in 6 Documents MSC: 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A15 Spline approximation 41A10 Approximation by polynomials Keywords:bivariate \(C^ 1\) piecewise cubic polynomial functions; full approximation order PDF BibTeX XML Cite \textit{M.-J. Lai}, Comput. Aided Geom. Des. 11, No. 2, 215--223 (1994; Zbl 0792.41023) Full Text: DOI References: [1] de Boor, C., B-form basics, (), 131-148 [2] Bramble, J.H.; Hilbert, S.R., Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. math., 16, 362-369, (1971) · Zbl 0214.41405 [3] de Boor, C.; Höllig, K., Approximation order from bivariate C1-cubics: a counterexample, Proc. amer. math. soc., 87, 649-655, (1983) · Zbl 0545.41017 [4] de Boor, C.; Höllig, K., Approximation power of smooth bivariate pp functions, Math. Z., 197, 343-363, (1988) · Zbl 0616.41010 [5] Chui, C.K., Multivariate splines, (1988), SIAM Philadelphia, PA · Zbl 0644.41007 [6] Farin, G., Triangular Bernstein-Bézier patches, Computer aided geometric design, 3, 83-127, (1986) [7] Jia, R.Q., Approximation order of smooth bivariate piecewise polynomial functions on a three-directional mesh, (1990), in manuscript This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.