Construction et validation des éléments Serendip associés á un carreau de degré arbitraire

Abstract : We give a method to constructing Serendipity elements for quads and hexes with full symmetry properties and indicate the reading of their shape functions. We show that, since the degree~5, the Serendipity elements are no longer symmetric but we propose a method resulting in a Lagrange element of degree 5 with full symmetry properties after adding an adequate number of additional nodes. On the other hand, we show how to guarantee the geometric validity of a given curved element (seen as a patch) of a mesh. This is achieved after writing the patch in a Bézier setting (Bernstein polynomials and control points). In addition, we discuss the case of patch derived from a transfinite interpolation and it is proved that only some of them are Serendipity elements indeed, we return to the same elements as above.
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Paul-Louis George, Houman Borouchaki, Nicolas Barral. Construction et validation des éléments Serendip associés á un carreau de degré arbitraire. [Rapport de recherche] RR-8572, INRIA. 2014, pp.107. ⟨hal-01052913⟩

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