Commit 11469e1c by 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, \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 yields the following 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} ... ...
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!