From 79c40c5eb9cf464ba0b2a66005b104b46b46520c Mon Sep 17 00:00:00 2001 From: buerg Date: Mon, 1 Nov 2010 17:15:28 +0000 Subject: [PATCH] Restored previous changes. git-svn-id: https://svn.dealii.org/trunk@22578 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/include/deal.II/fe/fe_nedelec.h | 48 ++++++++++++++++++++----- 1 file changed, 39 insertions(+), 9 deletions(-) diff --git a/deal.II/include/deal.II/fe/fe_nedelec.h b/deal.II/include/deal.II/fe/fe_nedelec.h index 89abf472dc..9d5c70cf36 100644 --- a/deal.II/include/deal.II/fe/fe_nedelec.h +++ b/deal.II/include/deal.II/fe/fe_nedelec.h @@ -1,3 +1,14 @@ +//--------------------------------------------------------------------------- +// $Id$ +// +// Copyright (C) 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 +// to the file deal.II/doc/license.html for the text and +// further information on this license. +// +//--------------------------------------------------------------------------- #ifndef __deal2__fe_nedelec_h #define __deal2__fe_nedelec_h @@ -22,14 +33,33 @@ template class MappingQ; /*@{*/ /** - * Implementation of Nédélec elements, conforming with the + * @warning Several aspects of the implementation are + * experimental. For the moment, it is safe to use the element on + * globally refined meshes with consistent orientation of faces. See + * the todo entries below for more detailed caveats. + * + * Implementation of Nédélec elements, conforming with the * space Hcurl. These elements generate vector fields with * tangential components continuous between mesh cells. * - * We follow the usual definition of the degree of Nédélec elements, - * which denotes the polynomial degree of the lowest complete polynomial - * subspace contained in the Nédélec space. Then, approximation order of - * the function itself is degree. + * We follow the convention that the degree of Nédélec elements + * denotes the polynomial degree of the largest complete polynomial subspace + * contained in the Nédélec space. This leads to the + * consistently numbered sequence of spaces + * @f[ + * Q_{k+1} + * \stackrel{\text{grad}}{\rightarrow} + * \text{Nedelec}_k + * \stackrel{\text{curl}}{\rightarrow} + * \text{RaviartThomas}_k + * \stackrel{\text{div}}{\rightarrow} + * DGQ_{k} + * @f] + * Consequently, approximation order of + * the Nedelec space equals the value degree given to the constructor. + * In this scheme, the lowest order element would be created by the call + * FE_Nedelec(0). Note that this follows the convention of Brezzi and + * Raviart, though not the one used in the original paper by Nedelec. * * This class is not implemented for the codimension one case * (spacedim != dim). @@ -42,7 +72,7 @@ template class MappingQ; *

Interpolation

* * The @ref GlossInterpolation "interpolation" operators associated - * with the Nédélec element are constructed such that interpolation and + * with the Nédélec element are constructed such that interpolation and * computing the curl are commuting operations. We require this * from interpolating arbitrary functions as well as the #restriction * matrices. @@ -51,7 +81,7 @@ template class MappingQ; * * The @ref GlossNodes "node values" on edges are the moments of the * tangential component of the interpolated function with respect to - * the traces of the Nédélec polynomials. Higher-order Nédélec spaces + * the traces of the Nédélec polynomials. Higher-order Nédélec spaces * also have face and interior nodes. * *

Generalized support points

@@ -64,13 +94,13 @@ template class MappingQ; * the interior of the cell (or none for N1). * * - * @author Markus Bürg, 2009 + * @author Markus Bürg, 2009 */ template class FE_Nedelec : public FE_PolyTensor, dim> { public: /** - * Constructor for the Nédélec + * Constructor for the Nédélec * element of degree @p p. */ FE_Nedelec (const unsigned int p); -- 2.39.5