From 4d3790df696285b3a370fd45b16483a4ae16c774 Mon Sep 17 00:00:00 2001 From: guido Date: Wed, 7 Jun 2006 14:04:57 +0000 Subject: [PATCH] add description of Gauss-Lobatto formula git-svn-id: https://svn.dealii.org/trunk@13191 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/base/include/base/quadrature_lib.h | 17 ++++++++++++++--- 1 file changed, 14 insertions(+), 3 deletions(-) diff --git a/deal.II/base/include/base/quadrature_lib.h b/deal.II/base/include/base/quadrature_lib.h index f869dc7bb3..291ef1e330 100644 --- a/deal.II/base/include/base/quadrature_lib.h +++ b/deal.II/base/include/base/quadrature_lib.h @@ -2,7 +2,7 @@ // $Id$ // Version: $Name$ // -// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005 by the deal.II authors +// 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 @@ -45,11 +45,22 @@ class QGauss : public Quadrature /** - * Gauss quadrature rule using the Gauss-Lobatto points. + * 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 2n-2, + * this formula is suboptimal by one degree. + * + * The quadrature points are interval end points plus the zeroes 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 The quadrature weights are not implemented yet. * - * @author Guido Kanschat, 2005 + * @sa http://en.wikipedia.org/wiki/Handbook_of_Mathematical_Functions + * + * @author Guido Kanschat, 2005, 2006 */ template class QGaussLobatto : public Quadrature -- 2.39.5