Loading...
Searching...
No Matches
<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 } };
Float
see the Float page for the full documentation
edge
see the edge page for the full documentation
point
see the point page for the full documentation
dimension
const size_t dimension
Definition edge.icc:64
vertex
const point vertex[n_vertex]
Definition edge.icc:67
n_vertex
const size_t n_vertex
Definition edge.icc:66
measure
const Float measure
Definition edge.icc:65
n_edge
const size_t n_edge
Definition hexahedron.icc:117