From d75fb6f1eb46793e683ebdf1471227473c5a3248 Mon Sep 17 00:00:00 2001
From: Kilian Weishaupt <kilian.weishaupt@iws.uni-stuttgart.de>
Date: Fri, 18 Dec 2015 06:57:48 +0100
Subject: [PATCH] [doc] Fix error in handbook
In the section where the assembly of the linear system is explained,
the RHS of the linear system should be the residual r(u) and not the
primary variable u itself. It should read J(u)*x=r(u).
---
doc/handbook/4_assemblinglinearsystem.tex | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/doc/handbook/4_assemblinglinearsystem.tex b/doc/handbook/4_assemblinglinearsystem.tex
index 1bdc41b425..fe790e4bdf 100644
--- a/doc/handbook/4_assemblinglinearsystem.tex
+++ b/doc/handbook/4_assemblinglinearsystem.tex
@@ -38,7 +38,7 @@ Each column is the residual derived with respect to the $m$th entry of $\textbf{
The Jacobian indicates the direction where the residual increases. By solving the
linear system
\begin{align*}
- J_{\textbf{r}(\textbf{u}^i)} \cdot \textbf{x}^i = \textbf{u}^i
+ J_{\textbf{r}(\textbf{u}^i)} \cdot \textbf{x}^i = \textbf{r}(\textbf{u}^i)
\end{align*}
we calculate the direction of maximum growth $\textbf{x}^i$. We subtract it from
our current solution to get a new, better solution
--
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