From 3b2658637350b0dc67d2f49abe2d1bbe6efe7005 Mon Sep 17 00:00:00 2001 From: bangerth Date: Wed, 15 Sep 2010 11:36:09 +0000 Subject: [PATCH] Multiple markup changes. git-svn-id: https://svn.dealii.org/trunk@21980 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/base/include/base/polynomial.h | 20 +++++++++++++++----- 1 file changed, 15 insertions(+), 5 deletions(-) diff --git a/deal.II/base/include/base/polynomial.h b/deal.II/base/include/base/polynomial.h index c9c4514c45..43b5925233 100644 --- a/deal.II/base/include/base/polynomial.h +++ b/deal.II/base/include/base/polynomial.h @@ -2,7 +2,7 @@ // $Id$ // Version: $Name$ // -// Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006 by the deal.II authors +// Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2010 by the deal.II authors // // This file is subject to QPL and may not be distributed // without copyright and license information. Please refer @@ -450,13 +450,23 @@ namespace Polynomials /** * Lobatto polynomials of arbitrary degree on [0,1]. * - * These polynomials are the integrated Legendre polynomials on [0,1]. The first two polynomials are the standard linear shape functions given by $l_0(x) = 1-x$ and $l_1(x) = x$. For $i\geq2$ we use the definition $l_i(x) = \frac{1}{\Vert L_{i-1}\Vert_2}\int_0^x L_{i-1}(t)\,dt, where L_i deontes the i-th Legendre polynomial on [0,1]. The Lobatto polynomials l_0,\ldots,l_k form a complete basis of the polynomials space of degree k. + * These polynomials are the integrated Legendre polynomials on [0,1]. The + * first two polynomials are the standard linear shape functions given by + * $l_0(x) = 1-x$ and $l_1(x) = x$. For $i\geq2$ we use the definition $l_i(x) + * = \frac{1}{\Vert L_{i-1}\Vert_2}\int_0^x L_{i-1}(t)\,dt$, where $L_i$ + * denotes the $i$-th Legendre polynomial on $[0,1]$. The Lobatto polynomials + * $l_0,\ldots,l_k$ form a complete basis of the polynomials space of degree + * $k$. * - * Calling the constructor with a given index k will generate the polynomial with index k. But only for $k\geq1$ the index equals the degree of the polynomial. For k==0 also a polynomial of degree 1 is generated. + * Calling the constructor with a given index k will generate the + * polynomial with index k. But only for $k\geq 1$ the index equals + * the degree of the polynomial. For k==0 also a polynomial of degree + * 1 is generated. * - * These polynomials are used for the construction of the shape functions of Nédélec elements of arbitrary order. + * These polynomials are used for the construction of the shape functions of + * Nédélec elements of arbitrary order. * - * @author Markus Bürg, 2009 + * @author Markus Bürg, 2009 */ class Lobatto : public Polynomial { public: -- 2.39.5