Reference documentation for deal.II version GIT relicensing-1399-g2b3a69e058 2024-08-09 08:50:02+00:00
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QGaussLobatto< dim > Class Template Reference

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.
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.

## ◆ 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: