Commit 11469e1c authored by Martin Schneider's avatar Martin Schneider

[handbook][box] Replace wrong scalar products in integrals

parent a900006d
......@@ -106,14 +106,13 @@ of the residual $\varepsilon$ with a weighting function $W_j$ and claiming that
this product has to vanish within the whole domain,
\begin{equation}
\int_\Omega W_j \cdot \varepsilon \, \mathrm{d}x \overset {!}{=} \: 0 \qquad \textrm{with} \qquad \sum_j W_j =1
\int_\Omega \varepsilon W_j \, \mathrm{d}x \overset {!}{=} \: 0 \qquad \textrm{with} \qquad \sum_j W_j =1
\end{equation}
yields the following equation:
\begin{equation}
\int_\Omega W_j \frac{\partial \tilde u}{\partial t} \, \mathrm{d}x + \int_\Omega W_j
\cdot \left[ \nabla \cdot F(\tilde u) \right] \, \mathrm{d}x - \int_\Omega W_j
\cdot q \, \mathrm{d}x = \int_\Omega W_j \cdot \varepsilon \, \mathrm{d}x \: \overset {!}{=} \: 0.
\int_\Omega \frac{\partial \tilde u}{\partial t} W_j \, \mathrm{d}x + \int_\Omega
\left[ \nabla \cdot F(\tilde u) \right] W_j \, \mathrm{d}x - \int_\Omega q W_j \, \mathrm{d}x = \int_\Omega \varepsilon W_j \, \mathrm{d}x \: \overset {!}{=} \: 0.
\label{eq:weightedResidual}
\end{equation}
......
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