NAME¶

triangle - reference element (rheolef-7.2)

DESCRIPTION¶

The triangle reference_element(6) is K = [0,1].

    K = { 0 < x0 < 1 and 0 < x1 < 1-x0 }


    x1


    2


    | +


    |   +


    |     +


    |       +


    0---------1  x0 

This two-dimensional reference_element(6) is then transformed, after the Piola geometrical application, as a triangle in a 2D or 3D physical space, as a geo_element(6).

Curved high order transformed geo_element(6) Pk triangle (k >= 1) are supported for 2D or 3D geometries. In these cases, the nodes of an high-order triangle are numbered as:

Note that high-order triangles have additional edge-nodes and face-nodes. These nodes are numbered as: first vertices, then edge-nodes, following the edge numbering order and orientation, and finally the face internal nodes, following the triangle lattice.

  2               2               2


  | +             | +             | +


  |   +           7   6           9   8


  5     4         |     +        10 14  7


  |       +       8   9   5      11 12 13 6


  |         +     |         +     |         +


  0-----3-----1   0---3---4---1   0--3--4--5--1


        P2              P3              P4

IMPLEMENTATION¶

This documentation has been generated from file fem/geo_element/triangle.icc

const size_t dimension = 2;
const Float  measure = 0.5;
const size_t n_vertex = 3;
const point vertex [n_vertex] = {


        point(0, 0),


        point(1, 0),


        point(0, 1) };
const size_t  n_edge = 3;
const size_t edge [n_edge][2] = {


        { 0, 1 },


        { 1, 2 },


        { 2, 0 } };

AUTHOR¶

Pierre Saramito <Pierre.Saramito@imag.fr>

COPYRIGHT¶

Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>. This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.