---
name: "quadrangle"
section: "6rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/quadrangle"
---

# quadrangle(6rheolef)

reference element (rheolef-7.2)

## NAME

quadrangle - reference element (rheolef-7.2)

## DESCRIPTION

The quadrangle **reference\_element(6)** is `K = [-1,1]^2`.

```
    x1
    3---------2
    |         |
    |         |
    |         |
    |         |
    0---------1--->  x0
```

 This two-dimensional **reference\_element(6)** is then transformed, after the Piola geometrical application, as a quadrangle in a 2D or 3D physical space, as a **geo\_element(6)**.

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 } };
```

## 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.