Rheolef  7.2
an efficient C++ finite element environment
 
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<tt>triangle</tt>

reference element

Description

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

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

    x1
    2
    | +
    |   +
    |     +
    |       +
    0---------1  x0 

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

Curved high order transformed geo_element 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 } };
see the Float page for the full documentation
see the edge page for the full documentation
see the point page for the full documentation
const size_t dimension
Definition edge.icc:64
const point vertex[n_vertex]
Definition edge.icc:67
const size_t n_vertex
Definition edge.icc:66
const Float measure
Definition edge.icc:65
const size_t n_edge