Construction de maillages de degré 2 - Partie 1 : Triangle P2

Paul-Louis George 1, * Houman Borouchaki 1 Patrick Laug 1
* Auteur correspondant
1 Gamma3 - Automatic mesh generation and advanced methods
Inria Paris-Rocquencourt, UTT - Université de Technologie de Troyes
Abstract : There is a need for finite elements of degree 2 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), restricting at degree 2. This first part 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. The surface case is detailed in the second part, and the volume case is seen in part three.
Type de document :
Rapport
[Rapport de recherche] RR-7519, INRIA. 2011
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Paul-Louis George, Houman Borouchaki, Patrick Laug. Construction de maillages de degré 2 - Partie 1 : Triangle P2. [Rapport de recherche] RR-7519, INRIA. 2011. 〈inria-00560529v2〉

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