Reference documentation for deal.II version GIT relicensing-464-g14f7274e4d 2024-04-22 15:40:02+00:00
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Public Member Functions | List of all members
QGaussLobatto< dim > Class Template Reference

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

Inheritance diagram for QGaussLobatto< dim >:
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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 Pn-1 of degree n-1. The quadrature weights are 2/(n(n-1)(Pn-1(xi)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.


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