From: kanschat Date: Sat, 23 Nov 2013 08:02:51 +0000 (+0000) Subject: change encoding to UTF-8 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=ba6a6970779e11a8a4e236dcee8208e407f1eb36;p=dealii-svn.git change encoding to UTF-8 git-svn-id: https://svn.dealii.org/trunk@31772 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/include/deal.II/base/quadrature.h b/deal.II/include/deal.II/base/quadrature.h index 58dd4fbc1d..688fc6aa32 100644 --- a/deal.II/include/deal.II/base/quadrature.h +++ b/deal.II/include/deal.II/base/quadrature.h @@ -29,16 +29,16 @@ DEAL_II_NAMESPACE_OPEN /*@{*/ /** - * Base class for quadrature formulæ in arbitrary dimensions. This class + * Base class for quadrature formulæ in arbitrary dimensions. This class * stores quadrature points and weights on the unit line [0,1], unit * square [0,1]x[0,1], etc. * * There are a number of derived classes, denoting concrete - * integration formulæ. Their names names prefixed by + * integration formulæ. Their names names prefixed by * Q. Refer to the list of derived classes for more details. * * The schemes for higher dimensions are typically tensor products of the - * one-dimensional formulæ, but refer to the section on implementation + * one-dimensional formulæ, but refer to the section on implementation * detail below. * * In order to allow for dimension independent programming, a @@ -48,7 +48,7 @@ DEAL_II_NAMESPACE_OPEN * point with weight one. Access to the weight is possible, while * access to the quadrature point is not permitted, since a Point of * dimension zero contains no information. The main purpose of these - * formulæ is their use in QProjector, which will create a useful + * formulæ is their use in QProjector, which will create a useful * formula of dimension one out of them. * *

Mathematical background

@@ -59,20 +59,20 @@ DEAL_II_NAMESPACE_OPEN * error is m+1, that is, the error is the size of the cell * to the m+1 by the Bramble-Hilbert Lemma. The number * m is to be found in the documentation of each concrete - * formula. For the optimal formulæ QGauss we have $m = 2N-1$, where + * formula. For the optimal formulæ QGauss we have $m = 2N-1$, where * N is the constructor parameter to QGauss. The tensor product - * formulæ are exact on tensor product polynomials of degree + * formulæ are exact on tensor product polynomials of degree * m in each space direction, but they are still only of * m+1st order. * *

Implementation details

* - * Most integration formulæ in more than one space dimension are - * tensor products of quadrature formulæ in one space dimension, or + * Most integration formulæ in more than one space dimension are + * tensor products of quadrature formulæ in one space dimension, or * more generally the tensor product of a formula in (dim-1) * dimensions and one in one dimension. There is a special constructor * to generate a quadrature formula from two others. For example, the - * QGauss@ formulæ include Ndim quadrature + * QGauss@ formulæ include Ndim quadrature * points in dim dimensions, where N is the constructor * parameter of QGauss. * @@ -330,7 +330,7 @@ public: * of the weights of the left- and the rightmost quadrature point. * * Since all dimensions higher than one are built up by tensor products of - * one dimensional and dim-1 dimensional quadrature formulæ, the + * one dimensional and dim-1 dimensional quadrature formulæ, the * argument given to the constructor needs to be a quadrature formula in * one space dimension, rather than in dim dimensions. * diff --git a/deal.II/include/deal.II/base/tensor_product_polynomials.h b/deal.II/include/deal.II/base/tensor_product_polynomials.h index 8f74b0aa68..bda2c89a97 100644 --- a/deal.II/include/deal.II/base/tensor_product_polynomials.h +++ b/deal.II/include/deal.II/base/tensor_product_polynomials.h @@ -320,7 +320,7 @@ private: unsigned int n_tensor_pols; /** - * Each tensor product polynomial @þ{i} is a product of one-dimensional + * Each tensor product polynomial @þ{i} is a product of one-dimensional * polynomials in each space direction. Compute the indices of these * one-dimensional polynomials for each space direction, given the index * i.