Completeness of generating systems for quadratic splines on adaptively refined criss cross triangulations
Hierarchical generating systems that are derived from Zwart Powell (ZP) elements can be used to generate quadratic splines on adaptively refined criss cross triangulations. We propose two extensions of these hierarchical generating systems, firstly decoupling the hierarchical ZP elements, and secondly enriching the system by including auxiliary functions. These extensions allow us to generate the entire hierarchical spline space which consists of all piecewise quadratic C 1 smooth functions on an adaptively refined criss cross triangulation if the triangulation fulfills certain technical assumptions. Special attention is dedicated to the characterization of the linear dependencies that are present in the resulting enriched decoupled hierarchical generating system. Hierarchical Zwart Powell elements are studied.Sufficient conditions for algebraic completeness are given.Construction uses decoupling and partial chessboard functions.Characterization of linear dependencies is provided.
Comput. Aided Geom. Des.