Section: New Results

Construction de maillages de degré 2 – Triangle et tétraèdre P2

Participants : P.L. George [correspondant], H. Borouchaki, P. Laug

There is a need for finite elements of degree 2 or more to solve various P.D.E. problems. This study 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 invalid elements are shown while proposing a method to correct them. A construction method is then proposed [34] .