Optimal Lagrange interpolation by quartic C 1 splines on triangulations

We develop a local Lagrange interpolation scheme for quartic C 1 splines on triangulations. Given an arbitrary triangulation Δ , we decompose Δ into pairs of neighboring triangles and add “diagonals” to some of these pairs. Only in exceptional cases, a few triangles are split. Based on this simple r...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2008-07, Vol.216 (2), p.344-363
Main Authors: Chui, C.K., Hecklin, G., Nürnberger, G., Zeilfelder, F.
Format: Article
Language:English
Subjects:
Bivariate splines
Local Lagrange interpolation
Optimal approximation order
Refinement of triangulations
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Summary:We develop a local Lagrange interpolation scheme for quartic C 1 splines on triangulations. Given an arbitrary triangulation Δ , we decompose Δ into pairs of neighboring triangles and add “diagonals” to some of these pairs. Only in exceptional cases, a few triangles are split. Based on this simple refinement of Δ , we describe an algorithm for constructing Lagrange interpolation points such that the interpolation method is local, stable and has optimal approximation order. The complexity for computing the interpolating splines is linear in the number of triangles. For the local Lagrange interpolation methods known in the literature, about half of the triangles have to be split.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2007.05.013