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 } };