From: Wolfgang Bangerth Date: Sun, 14 Feb 2010 00:04:23 +0000 (+0000) Subject: Fix typo. X-Git-Tag: v8.0.0~6452 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=0a171233bd5b6af153c1e220f0a8820e83a6b334;p=dealii.git Fix typo. git-svn-id: https://svn.dealii.org/trunk@20609 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-14/doc/intro.dox b/deal.II/examples/step-14/doc/intro.dox index 43187115fb..0f6004d52e 100644 --- a/deal.II/examples/step-14/doc/intro.dox +++ b/deal.II/examples/step-14/doc/intro.dox @@ -19,17 +19,17 @@ estimation and adaptivity for general functional output for the Laplace equation, while the second gives many examples of applications of these concepts to a large number of other, more complicated equations. For applications to individual types of equations, see also the publications by -Becker @ref step_14_Bec95 "[Bec95]", @ref step_14_Bec98 "[Bec98]", +Becker @ref step_14_Bec95 "[Bec95]", @ref step_14_Bec98 "[Bec98]", Kanschat @ref step_14_Kan96 "[Kan96]", @ref step_14_FK97 "[FK97]", Suttmeier @ref step_14_Sut96 "[Sut96]", @ref step_14_RS97 "[RS97]", @ref step_14_RS98c "[RS98c]", -@ref step_14_RS99 "[RS99]", -Bangerth @ref step_14_BR99b "[BR99b]", @ref step_14_Ban00w "[Ban00w]", -@ref step_14_BR01a "[BR01a]", @ref step_14_Ban02 "[Ban02]", and -Hartmann @ref step_14_Har02 "[Har02]", @ref step_14_HH01 "[HH01]", +@ref step_14_RS99 "[RS99]", +Bangerth @ref step_14_BR99b "[BR99b]", @ref step_14_Ban00w "[Ban00w]", +@ref step_14_BR01a "[BR01a]", @ref step_14_Ban02 "[Ban02]", and +Hartmann @ref step_14_Har02 "[Har02]", @ref step_14_HH01 "[HH01]", @ref step_14_HH01b "[HH01b]". All of these works, from the original introduction by Becker and Rannacher to individual contributions to particular equations, have later been summarized -in a book by Bangerth and Rannacher that covers all of these topics, see +in a book by Bangerth and Rannacher that covers all of these topics, see @ref step_14_BR03 "[BR03]". @@ -97,7 +97,7 @@ with which this term could cancel, the weight $z-\varphi_h$ can be chosen as zero, since $z$ has zero boundary values, and $\varphi_h$ can be chosen to have the same. -Thus, we have +Thus, we have @f{eqnarray*} J(e) &=& @@ -114,7 +114,7 @@ with the neighbor cell $K'$, to obtain &=& \sum_K (f+\Delta u_h, z-\varphi_h)_K - \frac 12 (\partial_n u_h|_K + \partial_{n'} u_h|_{K'}, - z-\varphi_h)_{\partial K\backslash \partial\Omega}. + z-\varphi_h)_{\partial K\backslash \partial\Omega}. @f} Using that for the normal vectors $n'=-n$ holds, we define the jump of the normal derivative by @@ -131,7 +131,7 @@ $\varphi_h=I_h z$: &=& \sum_K (f+\Delta u_h, z-I_h z)_K - \frac 12 ([\partial_n u_h], - z-I_h z)_{\partial K\backslash \partial\Omega}. + z-I_h z)_{\partial K\backslash \partial\Omega}. @f} With this, we have obtained an exact representation of the error of the finite @@ -316,7 +316,7 @@ example program.
Roland Becker and Rolf Rannacher.
Weighted a posteriori error control in FE methods.
In H. G. Bock et al., ed.s, ENUMATH 95, pages 621–637, - Paris, September 1998. World Scientific Publ., Singapure. + Paris, September 1998. World Scientific Publ., Singapore.
in @ref step_14_enumath97 "[enumath97]".