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# quadrangle - Quadrangular reference element

 quadrangle(7rheolef) rheolef-6.7 quadrangle(7rheolef)

## NAME

quadrangle - Quadrangular reference element

## DESCRIPTION

The quadrangular reference element is [-1,1]^2.

## NUMBERING

```      y
```
```      3---------2
|         |
|         |
|         |
|         |
0---------1   x

```
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. See below for edge numbering and orientation.

```      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

```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 } };

```
 rheolef-6.7 rheolef-6.7