From: Wolfgang Bangerth <bangerth@math.tamu.edu>
Date: Wed, 6 Jul 2016 16:14:51 +0000 (-0500)
Subject: Better connect step-56 throughout the tutorials.
X-Git-Tag: v8.5.0-rc1~924^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F2752%2Fhead;p=dealii.git

Better connect step-56 throughout the tutorials.
---

diff --git a/examples/step-16/doc/results.dox b/examples/step-16/doc/results.dox
index f1835761b5..bf6d2a96e5 100644
--- a/examples/step-16/doc/results.dox
+++ b/examples/step-16/doc/results.dox
@@ -78,6 +78,13 @@ it becomes even more difficult if the program is to run in %parallel on
 machines coupled through MPI, for example. In that case, it would be
 simpler if one could use a black-box preconditioner that uses some
 sort of multigrid hierarchy for good performance but can figure out
-level matrices and similar things out by itself. Algebraic multigrid
+level matrices and similar things by itself. Algebraic multigrid
 methods do exactly this, and we will use them in
-step-31 for the solution of a Stokes problem.
+step-31 for the solution of a Stokes problemm and in step-32 and
+step-40 for a parallel variation.
+
+Finally, one may want to think how to use geometric multigrid for
+other kinds of problems, specifically 
+@ref vector_valued "vector valued problems". This is the topic of
+step-56 where we use the techniques shown here for the Stokes
+equation.
diff --git a/examples/step-22/doc/results.dox b/examples/step-22/doc/results.dox
index 52868456a1..52af0f34ed 100644
--- a/examples/step-22/doc/results.dox
+++ b/examples/step-22/doc/results.dox
@@ -727,12 +727,15 @@ because GMRES(k) scales worse with the problem size than CG, as we discussed
 above.  Nonetheless, the improvement by a factor of 3-6 for moderate problem
 sizes is quite impressive.
 
-<h5>Combining block preconditioner and multigrid</h5>
+
+<h5>Combining the block preconditioner and multigrid</h5>
 An ultimate linear solver for this problem could be imagined as a
 combination of an optimal
 preconditioner for $A$ (e.g. multigrid) and the block preconditioner
 described above, which is the approach taken in the step-31
-tutorial program.
+and step-32 tutorial programs (where we use an algebraic multigrid
+method) and step-56 (where we use a geometric multigrid method).
+
 
 <h5>No block matrices and vectors</h5>
 Another possibility that can be taken into account is to not set up a block