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<tt>quadrangle</tt>

reference element

# Description

The quadrangle `reference_element` is `K = [-1,1]^2`.

        x1

        3---------2
        |         |
        |         |
        |         |
        |         |
        0---------1--->  x0

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

Curved high order Pk quadrangles (k >= 1), in 2D or 3D geometries, are supported. These quadrangles 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 quadrangle lattice.

        3-----6-----2   3---9---8---2
        |           |   |           |
        |           |  10  14  15   7
        7     8     5   |           |
        |           |  11  12  13   6
        |           |   |           |
        0-----4-----1   0---4---5---1
              P2              P3

# Implementation

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

const size_t dimension = 2;
const Float measure = 4;
const size_t n_vertex = 4;
const point vertex [n_vertex] = {
point(-1,-1),
point( 1,-1),
point( 1, 1),
point(-1, 1) };
const size_t n_edge = 4;
const size_t edge [n_edge][2] = {
{ 0, 1 },
{ 1, 2 },
{ 2, 3 },
{ 3, 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