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triangle - Triangle reference element

triangle(7rheolef) rheolef-6.7 triangle(7rheolef)

NAME

triangle - Triangle reference element

DESCRIPTION

The triangle reference element is
 
        K = { 0 < x < 1 and 0 < y < 1-x }
 

NUMBERING

      y
      2
      | +
      |   +
      |     +
      |       +
      0---------1   x
 
Curved high order Pk triangles (k >= 1), in 2d or 3d geometries, are supported. These triangles have additional edge-nodes and face-nodes.

THESE NODES ARE NUMBERED AS


first vertex, then edge-node, following the edge numbering order and orientation, and finally the face internal nodes, following the triangle lattice. See below for edge numbering and orientation.
 
      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

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 } };
 
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