minor edits to step 4, including typos and clarification on solution verification

diff --git a/examples/step-4/doc/intro.dox b/examples/step-4/doc/intro.dox
index e554c4944c91c34626156684d2bc24003beb7c9b..7c7eef54a0c1b8fb3402af261975f0149b58cc5e 100644 (file)
--- a/examples/step-4/doc/intro.dox
+++ b/examples/step-4/doc/intro.dox
@@ -111,7 +111,7 @@ amount of memory for the member variable; note that the size of a
 
 
 
-The deal.II library is build around this concept
+The deal.II library is built around this concept
 of dimension-independent programming, and therefore allows you to program in
 a way that will not need to
 distinguish between the space dimensions. It should be noted that in

diff --git a/examples/step-4/doc/results.dox b/examples/step-4/doc/results.dox
index 44dffe84897eea06409273d9465f231d893d7326..f5bd1906de929af30c1247e96d10b81dab83cc58 100644 (file)
--- a/examples/step-4/doc/results.dox
+++ b/examples/step-4/doc/results.dox
@@ -53,6 +53,8 @@ maximal values of the right hand side function are at the corners of
 the domain, where also the solution is moving most rapidly.
 It is also nice to see that the solution follows the desired quadratic
 boundary values along the boundaries of the domain.
+It can also be useful to verify a computed solution against an analytical
+solution. For an explanation of this technique, see step-7.
 
 On the other hand, even though the picture does not show the mesh lines
 explicitly, you can see them as little kinks in the solution. This clearly
@@ -80,7 +82,7 @@ so that it is possible to see through them and see what's behind.
 </table>
 
 @note
-A final remark on visualization: The idea of visualization is to give insight,
+A final remark on visualization: the idea of visualization is to give insight,
 which is not the same as displaying information. In particular, it is easy to
 overload a picture with information, but while it shows more information it
 makes it also more difficult to glean insight. As an example, the program I
@@ -92,7 +94,7 @@ of this is important
 here: the axes are equally easy to make out because the tripod at the bottom
 left is still visible, and we know from the program that the domain is
 $[-1,1]^3$, so there is no need for tick marks. As a consequence, I have
-switched off all the extraneous stuff in the picture: The art of visualization
+switched off all the extraneous stuff in the picture: the art of visualization
 is to reduce the picture to those parts that are important to see what one
 wants to see, but no more.