QGaussLobatto< dim > Class Template Reference

#include <deal.II/base/quadrature_lib.h>

Inheritance diagram for QGaussLobatto< dim >:

Public Member Functions
	QGaussLobatto (const unsigned int n)
	QGaussLobatto (const unsigned int)

Detailed Description

template<int dim>
class QGaussLobatto< dim >

The Gauss-Lobatto family of quadrature rules for numerical integration.

This modification of the Gauss quadrature uses the two interval end points as well. Being exact for polynomials of degree 2n-3, this formula is suboptimal by two degrees.

The quadrature points are interval end points plus the roots of the derivative of the Legendre polynomial P_n-1 of degree n-1. The quadrature weights are 2/(n(n-1)(P_n-1(x_i)²).

Note

This implementation has not been optimized concerning numerical stability and efficiency. It can be easily adapted to the general case of Gauss-Lobatto-Jacobi-Bouzitat quadrature with arbitrary parameters \(\alpha\), \(\beta\), of which the Gauss-Lobatto-Legendre quadrature ( \(\alpha = \beta = 0\)) is a special case.

See also

http://en.wikipedia.org/wiki/Handbook_of_Mathematical_Functions

Karniadakis, G.E. and Sherwin, S.J.: Spectral/hp element methods for computational fluid dynamics. Oxford: Oxford University Press, 2005

Definition at line 139 of file quadrature_lib.h.

Constructor & Destructor Documentation

QGaussLobatto() [1/2]

template<int dim>

QGaussLobatto< dim >::QGaussLobatto

(

const unsigned int

n

)

Generate a formula with n quadrature points (in each space direction).

Definition at line 1064 of file quadrature_lib.cc.

QGaussLobatto() [2/2]

QGaussLobatto< 0 >::QGaussLobatto

(

const unsigned int

)

Definition at line 56 of file quadrature_lib.cc.

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The documentation for this class was generated from the following files:

• include/deal.II/base/quadrature_lib.h
• source/base/quadrature_lib.cc