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Construction de maillages de degré 2- Partie 3 : Tétraèdre P2

Abstract : There is a need for finite elements of degree two or more to solve various P.D.E. problems. This report in three parts discusses a method to construct such meshes in the case of triangular element (in the plane or for a surface) or tetrahedral element (in the volume case) by looking at the degree 2. \par The first part of this paper, \cite{bibtriap2}, considers the planar case and, to begin with, returns to Bézier curves and Bézier triangles of degree 2. In the case of triangles, the relation with Lagrange P2 finite element is shown. Validity conditions are discussed and some unvalid elements are shown while proposing a method to correct them. A construction method is then proposed and several application examples are given. \par This third part considers the case of P2 tetrahedra following the same organization as in part 1. Bézier curves, triangles and tetrahedra are briefly recalled. The way in which a Bézier tetrahedron and a P2 finite element tetrahedron are related is introduced. A validity condition is then exhibited. Extension to arbitrary degree and dimension is proposed while giving the reading of the corresponding formula. Then we return to the P2 tetrahedron and a construction method is proposed and demonstrated by means of various concrete application examples.
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https://hal.inria.fr/inria-00595759
Contributor : Paul-Louis George <>
Submitted on : Wednesday, May 25, 2011 - 2:56:18 PM
Last modification on : Wednesday, September 15, 2021 - 3:17:12 PM
Long-term archiving on: : Friday, November 9, 2012 - 12:10:45 PM

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Paul-Louis George, Houman Borouchaki. Construction de maillages de degré 2- Partie 3 : Tétraèdre P2. [Rapport de recherche] RR-7626, INRIA. 2011, pp.54. ⟨inria-00595759⟩

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