doxygen: use coloneq in tutorials

diff --git a/examples/step-61/doc/intro.dox b/examples/step-61/doc/intro.dox
index d58cd7a8c03712fe174e6a32670161ea74afd7f8..017883dbfdada579bd721bd79d9edd09e9e38239 100644 (file)
--- a/examples/step-61/doc/intro.dox
+++ b/examples/step-61/doc/intro.dox
@@ -102,12 +102,12 @@ formulation of the problem,
 for all test functions $q$, where
 @f{equation*}
 \mathcal{A}\left(p,q\right)
-  := \int_\Omega \left(\mathbf{K} \nabla p\right) \cdot \nabla q \;\mathrm{d}x,
+  \dealcoloneq \int_\Omega \left(\mathbf{K} \nabla p\right) \cdot \nabla q \;\mathrm{d}x,
 @f}
 and 
 @f{equation*}
 \mathcal{F}\left(q\right)
-  := \int_\Omega f \, q \;\mathrm{d}x
+  \dealcoloneq \int_\Omega f \, q \;\mathrm{d}x
   - \int_{\Gamma^N} u_N q \; \mathrm{d}x.
 @f}
 Here, we have integrated by parts in the bilinear form, and we are evaluating 
@@ -139,13 +139,13 @@ that is only defined in cell interiors. Consequently,
 for all discrete test functions $q_h$, where
 @f{equation*}
 \mathcal{A}_h\left(p_h,q_h\right)
-  := \sum_{K \in \mathbb{T}}
+  \dealcoloneq \sum_{K \in \mathbb{T}}
     \int_K \mathbf{K} \nabla_{w,d} p_h \cdot \nabla_{w,d} q_h \;\mathrm{d}x,
 @f}
 and 
 @f{equation*}
 \mathcal{F}\left(q_h\right)
-  := \sum_{K \in \mathbb{T}} \int_K f \, q_h^\circ \;\mathrm{d}x
+  \dealcoloneq \sum_{K \in \mathbb{T}} \int_K f \, q_h^\circ \;\mathrm{d}x
   - \sum_{\gamma \in \Gamma_h^N} \int_\gamma u_N q_h^\partial \;\mathrm{d}x,
 @f}
 The key point is that here, we have replaced the gradient $\nabla p_h$ by the

diff --git a/examples/step-63/doc/intro.dox b/examples/step-63/doc/intro.dox
index 04a6fb1736b36aa88ee18734442fe333c6efb824..59c71cf4566fd5c3fbac9047556282df3ed2a794 100644 (file)
--- a/examples/step-63/doc/intro.dox
+++ b/examples/step-63/doc/intro.dox
@@ -35,7 +35,7 @@ direction</i>, and $f$ is a source. A few notes:
 2. If $\varepsilon=0$ then this is the stationary advection equation solved in
 step-9.
 
-3. Define the <i>Peclet number</i>: $\mathcal{P}\:=\|\boldsymbol{\beta}\|
+3. Define the <i>Peclet number</i>: $\mathcal{P} \dealcoloneq \|\boldsymbol{\beta}\|
 \cdot L/\varepsilon$. If $\mathcal{P}>1$, we say the problem is
 <i>advection-dominated</i>, else if $\mathcal{P}<1$ we will say the problem is
 <i>diffusion-dominated</i>. Here $L$ is the length scale of the domain.