.TH "quadrangle" 6rheolef "Sat Mar 13 2021" "Version 7.1" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
quadrangle \- reference element (rheolef-7\&.1)
.PP
.SH "DESCRIPTION"
.PP
The quadrangle \fBreference_element(6)\fP is \fCK = [-1,1]^2\fP\&. 
.PP
.nf
    x1

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

.fi
.PP
 This two-dimensional \fBreference_element(6)\fP is then transformed, after the Piola geometrical application, as a quadrangle in a 2D or 3D physical space, as a \fBgeo_element(6)\fP\&.
.PP
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\&. 
.PP
.nf
    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

.fi
.PP
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file fem/geo_element/quadrangle\&.icc
.PP
.PP
.nf
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 } };
.fi
.PP

.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH 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.