ref_quadrilateral.hpp File Reference

Defines the reference quadrilateral element used in nodal Discontinuous Galerkin methods. More...

#include <xtensor/core/xtensor_forward.hpp>
#include "oiseau/dg/nodal/ref_element.hpp"

Go to the source code of this file.

Classes
class	oiseau::dg::nodal::RefQuadrilateral
	Represents a reference quadrilateral element for nodal Discontinuous Galerkin methods. More...

Functions
xt::xarray< double >	oiseau::dg::nodal::detail::generate_quadrilateral_nodes (unsigned order)
	Generates tensor-product Gauss-Lobatto nodes on the reference quadrilateral.

Detailed Description

Defines the reference quadrilateral element used in nodal Discontinuous Galerkin methods.

This file contains the declaration of the RefQuadrilateral class, which represents a reference square element, and associated internal helper functions in the detail namespace for generating nodes and performing coordinate transformations.

Node layout (order = 2):

s ↑ | | (6)——(7)——(8) | | | | | (3)——(4)——(5) | | | | | (0)——(1)——(2) +——————→ r

Nodes are numbered in lexicographic order from bottom-left to top-right.

Function Documentation

generate_quadrilateral_nodes()

xt::xarray< double > oiseau::dg::nodal::detail::generate_quadrilateral_nodes

(

unsigned

order

)

Generates tensor-product Gauss-Lobatto nodes on the reference quadrilateral.

Computes the 1D Gauss-Lobatto points of the given order and forms the tensor grid.

Parameters

order

Polynomial order (number of points per direction = order+1).

Returns

2D array ( (order+1)^2 × 2 ) of (r, s) node coordinates.