Abstract
Letτ be the triangulation generated by a uniform three direction mesh of the plane. Letτ 6 be the Powell-Sabin subtriangulation obtained by subdividing each triangleT ∈τ by connecting each vertex to the midpoint of the opposite side.
Given a smooth functionu, we construct a piecewise polynomial functionυ ∈C r (ℝ2) of degreen=2r (resp. 2r+1) forr odd (resp. even) in each triangle ofτ 6, interpolating derivatives ofu up to orderr at the vertices ofτ.
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Laghchim-Lahlou, M., Sablonnière, P. C r-finite elements of Powell-Sabin type on the three direction mesh. Adv Comput Math 6, 191–206 (1996). https://doi.org/10.1007/BF02127703
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DOI: https://doi.org/10.1007/BF02127703