From 9c2a81a68a9a16c14f5ecd23b7b217ff63e513ea Mon Sep 17 00:00:00 2001 From: wolf Date: Thu, 30 Jan 2003 02:38:50 +0000 Subject: [PATCH] Fix maths. git-svn-id: https://svn.dealii.org/trunk@6991 0785d39b-7218-0410-832d-ea1e28bc413d --- .../chapter-2.step-by-step/step-14.data/intro.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/intro.tex b/deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/intro.tex index accc91cb6b..4241f55074 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/intro.tex +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/intro.tex @@ -5,7 +5,7 @@ \section{The maths} The Heidelberg group of Professor Rolf Rannacher, to which the three main -authors of the deal.II library belonged for the PhD time and partly also +authors of the deal.II library belonged during their PhD time and partly also afterwards, has been involved with adaptivity and error estimation for finite element discretizations since the mid-90ies. The main achievement is the development of error estimates for arbitrary functionals of the solution, and @@ -92,7 +92,7 @@ Thus, we have \begin{align*} J(e) &= - \sum_K (f+u_h), z-\varphi_h)_K + \sum_K (f+\Delta u_h, z-\varphi_h)_K - (\partial_n u_h, z-\varphi_h)_{\partial K\backslash \partial\Omega}. \end{align*} In a final step, note that when taking the normal derivative of $u_h$, we mean @@ -103,7 +103,7 @@ with the neighbor cell $K'$, to obtain \begin{align*} J(e) &= - \sum_K (f+u_h), z-\varphi_h)_K + \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}. \end{align*} @@ -120,7 +120,7 @@ $\varphi_h=I_h z$: \begin{align*} J(e) &= - \sum_K (f+u_h), z-I_h z)_K + \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}. \end{align*} -- 2.39.5