<commit_before>//---------------------------------------------------------------------------
//    $Id$
//    Version: $Name$
//
//    Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005 by the deal.II authors
//
//    This file is subject to QPL and may not be  distributed
//    without copyright and license information. Please refer
//    to the file deal.II/doc/license.html for the  text  and
//    further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__quadrature_lib_h
#define __deal2__quadrature_lib_h


#include <base/config.h>
#include <base/quadrature.h>


/*!@addtogroup Quadrature */
/*@{*/

/**
 * Gauss-Legendre quadrature of arbitrary order.
 *
 * The coefficients of these quadrature rules are computed by the
 * function found in <tt>Numerical Recipies</tt>.
 *
 * @author <NAME>, 2001
 */
template <int dim>
class QGauss : public Quadrature<dim>
{
  public:
				   /**
				    * Generate a formula with
				    * <tt>n</tt> quadrature points (in
				    * each space direction), exact for
				    * polynomials of degree
				    * <tt>2n-1</tt>.
				    */
    QGauss (const unsigned int n);
};


/**
 * Gauss quadrature rule using the Gauss-Lobatto points.
 *
 * @note The quadrature weights are not implemented yet.
 *
 * @author <NAME>, 2005
 */
template<int dim>
class QGaussLobatto : public Quadrature<dim>
{
  public:
				     /**
				      * Generate a formula with
				      * <tt>n</tt> quadrature points
				      * (in each space direction).
				      */
    QGaussLobatto(const unsigned int n);
};

  

/**
 * @deprecated Use QGauss for arbitrary order Gauss formulae instead!
 *
 *  2-Point-Gauss quadrature formula, exact for polynomials of degree 3.
 *
 *  Reference: <NAME>, <NAME>: "Numerical Mathematics and Computing".
 *  For a comprehensive list of Gaussian quadrature formulae, see also:
 *  <NAME>, <NAME>: "Gaussian Quadrature Formulas"
 */
template <int dim>
class QGauss2 : public Quadrature<dim>
{
  public:
    QGauss2 ();
};<commit_msg>add description of Gauss-Lobatto formula<commit_after>//---------------------------------------------------------------------------
//    $Id$
//    Version: $Name$
//
//    Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006 by the deal.II authors
//
//    This file is subject to QPL and may not be  distributed
//    without copyright and license information. Please refer
//    to the file deal.II/doc/license.html for the  text  and
//    further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__quadrature_lib_h
#define __deal2__quadrature_lib_h


#include <base/config.h>
#include <base/quadrature.h>


/*!@addtogroup Quadrature */
/*@{*/

/**
 * Gauss-Legendre quadrature of arbitrary order.
 *
 * The coefficients of these quadrature rules are computed by the
 * function found in <tt>Numerical Recipies</tt>.
 *
 * @author <NAME>, 2001
 */
template <int dim>
class QGauss : public Quadrature<dim>
{
  public:
				   /**
				    * Generate a formula with
				    * <tt>n</tt> quadrature points (in
				    * each space direction), exact for
				    * polynomials of degree
				    * <tt>2n-1</tt>.
				    */
    QGauss (const unsigned int n);
};


/**
 * The Gauss-Lobatto quadrature rule.
 *
 * This modification of the Gauss quadrature uses the two interval end
 * points as well. Being exact for polynomials of degree <i>2n-2</i>,
 * this formula is suboptimal by one degree.
 *
 * The quadrature points are interval end points plus the zeroes of
 * the derivative of the Legendre polynomial <i>P<sub>n-1</sub></i> of
 * degree <i>n-1</i>. The quadrature weights are
 * <i>2/(n(n-1)(P<sub>n-1</sub>(x<sub>i</sub>)<sup>2</sup>)</i>.
 *
 * @note The quadrature weights are not implemented yet.
 *
 * @sa http://en.wikipedia.org/wiki/Handbook_of_Mathematical_Functions
 *
 * @author <NAME>, 2005, 2006
 */
template<int dim>
class QGaussLobatto : public Quadrature<dim>
{
  public:
				     /**
				      * Generate a formula with
				      * <tt>n</tt> quadrature points
				      * (in each space direction).
				      */
    QGaussLobatto(const unsigned int n);
};

  

/**
 * @deprecated Use QGauss for arbitrary order Gauss formulae instead!
 *
 *  2-Point-Gauss quadrature formula, exact for polynomials of degree 3.
 *
 *  Reference: <NAME>, <NAME>: "Numerical Mathematics and Computing".
 *  For a comprehensive list of Gaussian quadrature formulae, see also:
 *  <NAME>, <NAME>: "Gaussian Quadrature Formulas"
 */
template <int dim>
class QGauss2 : public Quadrature<dim>
{
  public:
    QGauss2 ();
};
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