From 5377bee361daf7ebf55318cf8f158b71b11682e0 Mon Sep 17 00:00:00 2001
From: Timo Heister <timo.heister@gmail.com>
Date: Wed, 15 May 2019 09:50:53 -0600
Subject: [PATCH] followup small step-63 edits

---
 examples/step-63/doc/intro.dox   | 9 ++++-----
 examples/step-63/doc/results.dox | 8 ++++----
 examples/step-63/step-63.cc      | 2 +-
 3 files changed, 9 insertions(+), 10 deletions(-)

diff --git a/examples/step-63/doc/intro.dox b/examples/step-63/doc/intro.dox
index f12dcad9a9..04a6fb1736 100644
--- a/examples/step-63/doc/intro.dox
+++ b/examples/step-63/doc/intro.dox
@@ -35,11 +35,10 @@ 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>: $\mathcal{P}\coloneqq
-\|\boldsymbol{\beta}\| \cdot L/\varepsilon$. 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.
+3. Define the <i>Peclet number</i>: $\mathcal{P}\:=\|\boldsymbol{\beta}\|
+\cdot L/\varepsilon$. 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.
 
 For the discussion in this tutorial we will be concerned with
 advection-dominated flow. 
diff --git a/examples/step-63/doc/results.dox b/examples/step-63/doc/results.dox
index 76ca966d88..c0136e509c 100644
--- a/examples/step-63/doc/results.dox
+++ b/examples/step-63/doc/results.dox
@@ -455,10 +455,10 @@ comparison of solve times for a $Q_3$ element with 74,496 DoFs:
 </tr>
 <tr>
   <th>74496</th>
-  <td>0.689 s</th>
-  <td>5.826 s</th>
-  <td>1.189 s</th>
-  <td>1.021 s</th>
+  <td>0.68s</th>
+  <td>5.82s</th>
+  <td>1.18s</th>
+  <td>1.02s</th>
 </tr>
 </table>
 
diff --git a/examples/step-63/step-63.cc b/examples/step-63/step-63.cc
index 4efa00baad..47654ac2ab 100644
--- a/examples/step-63/step-63.cc
+++ b/examples/step-63/step-63.cc
@@ -450,7 +450,7 @@ namespace Step63
   // from <a
   // href="https://link.springer.com/chapter/10.1007/978-3-540-34288-5_27"> On
   // Discontinuity-Capturing Methods for Convection-Diffusion Equations by
-  // Volker John and Petr Knobloch</a>
+  // Volker John and Petr Knobloch</a>.
   template <int dim>
   double compute_stabilization_delta(const double         hk,
                                      const double         eps,
-- 
2.39.5