Fix missing closing braces.

diff --git a/examples/step-47/doc/results.dox b/examples/step-47/doc/results.dox
index a2b0ad71d99a22666ec105863aa568a0e82503e0..088d096cc00a71925ae4ea4f105b9f80a0954556 100644 (file)
--- a/examples/step-47/doc/results.dox
+++ b/examples/step-47/doc/results.dox
@@ -240,18 +240,18 @@ make sense:
   @f}
   and by the definition of jump over cell interfaces,
   @f{align*}{
-  -\sum_{K \in \mathbb{T}} \int_{\partial K} (\nabla v_h) \cdot (\frac{\partial \nabla u_h}{\partial \mathbf{n}}) = -\sum_{e \in \mathbb{F}} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}} (\frac{\partial^2 u_h}{\partial \mathbf{n^2}}).
+  -\sum_{K \in \mathbb{T}} \int_{\partial K} (\nabla v_h) \cdot (\frac{\partial \nabla u_h}{\partial \mathbf{n}}) = -\sum_{e \in \mathbb{F}} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}}} (\frac{\partial^2 u_h}{\partial \mathbf{n^2}}).
   @f}
   We separate interior faces and boundary faces of the domain,
   @f{align*}{
-  -\sum_{K \in \mathbb{T}} \int_{\partial K} (\nabla v_h) \cdot (\frac{\partial \nabla u_h}{\partial \mathbf{n}}) = -\sum_{e \in \mathbb{F}^i} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}} (\frac{\partial^2 u_h}{\partial \mathbf{n^2}})
-  - \sum_{e \in \partial \Omega} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}} h,
+  -\sum_{K \in \mathbb{T}} \int_{\partial K} (\nabla v_h) \cdot (\frac{\partial \nabla u_h}{\partial \mathbf{n}}) = -\sum_{e \in \mathbb{F}^i} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}}} (\frac{\partial^2 u_h}{\partial \mathbf{n^2}})
+  - \sum_{e \in \partial \Omega} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}}} h,
   @f}
   where $\mathbb{F}^i$ is the set of interior faces.
   This leads us to
   @f{align*}{
-  \sum_{K \in \mathbb{T}} \int_K (D^2 v_h) : (D^2 u_h) \ dx - \sum_{e \in \mathbb{F}^i} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}} (\frac{\partial^2 u_h}{\partial \mathbf{n^2}}) \ ds
-  = \sum_{K \in \mathbb{T}}\int_{K} v_h f  \ dx + \sum_{e\subset\partial\Omega} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}} h \ ds.
+  \sum_{K \in \mathbb{T}} \int_K (D^2 v_h) : (D^2 u_h) \ dx - \sum_{e \in \mathbb{F}^i} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}}} (\frac{\partial^2 u_h}{\partial \mathbf{n^2}}) \ ds
+  = \sum_{K \in \mathbb{T}}\int_{K} v_h f  \ dx + \sum_{e\subset\partial\Omega} \int_{e} \jump{\frac{\partial v_h}{\partial \mathbf{n}}} h \ ds.
   @f}
 
   In order to symmetrize and stabilize the discrete problem,