TY - JOUR
AU1 - Davydov, O.
AU2 - Nürnberger, G.
AU3 - Zeilfelder, F.
AB - Let Δ be a triangulation of some polygonal domain Ω ⊂ R2 and let Sqr(Δ) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to Δ. We develop the first Hermite-type interpolation scheme for Sqr(Δ), q ≥ 3r + 2, whose approximation error is bounded above by Khq+1, where h is the maximal diameter of the triangles in Δ, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and near-singular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sqr(Δ). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [7] and [18].
TI - Bivariate spline interpolation with optimal approximation order
JF - Constructive Approximation
DO - 10.1007/s003650010034
DA - 2001-01-01
UR - https://www.deepdyve.com/lp/springer-journals/bivariate-spline-interpolation-with-optimal-approximation-order-nIU3D300aR
SP - 181
EP - 208
VL - 17
IS - 2
DP - DeepDyve
ER -