Interpolation with C2 quartic macro-elements based on 10-splits

[摘要] In this paper interpolation methods for the construction of quartic splines on triangulations refined with 10-splits are proposed. After examining the C-2 macro-structure on a single triangle in terms of the Bernstein-Bezier representation, three methods that can be applied on general triangulations are developed. The methods make use of Hermite interpolation data prescribed at the vertices and (optionally) on the edges of the triangulation. The first two approaches lead to splines that are C-2 continuous on triangles and C-1 continuous across the interior edges of the triangulation. The third method gives rise to splines with overall C-2 continuity, which is an exceptionally high order of smoothness for splines of degree four, but comes at the cost of solving a global system of linear equations. The derived results are accompanied with a few numerical examples that show an interesting behavior of splines in dependence of interpolated data. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-15

[关键词] C-2 quartic splines on triangulations;Macro-elements;10-split;Interpolation