From ca084abe3fd0fa87fd8b0b3aa352a7903e2c9723 Mon Sep 17 00:00:00 2001
From: bangerth <bangerth@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Wed, 8 Aug 2007 21:35:43 +0000
Subject: [PATCH] More text

git-svn-id: https://svn.dealii.org/trunk@14925 0785d39b-7218-0410-832d-ea1e28bc413d
---
 deal.II/examples/step-27/doc/intro.dox   | 15 +++++++++------
 deal.II/examples/step-27/doc/results.dox | 19 +++++++++++++++++++
 2 files changed, 28 insertions(+), 6 deletions(-)

diff --git a/deal.II/examples/step-27/doc/intro.dox b/deal.II/examples/step-27/doc/intro.dox
index 32fd970d61..bd4c1237bb 100644
--- a/deal.II/examples/step-27/doc/intro.dox
+++ b/deal.II/examples/step-27/doc/intro.dox
@@ -574,12 +574,15 @@ this tutorial program.
 
 <h4>Eliminating constrained degrees of freedom</h4>
 
-A second problem particular to $hp$ methods arises because we have so many
-constrained degrees of freedom: typically up to about one third of all degrees
-of freedom (in 3d) are constrained because they either belong to cells with
-hanging nodes or because they are on cells adjacent to cells with a higher or
-lower polynomial degree. This is much more than the fraction of constrained
-degrees of freedom in non-$hp$ mode.
+A second problem particular to $hp$ methods arises because we have so
+many constrained degrees of freedom: typically up to about one third
+of all degrees of freedom (in 3d) are constrained because they either
+belong to cells with hanging nodes or because they are on cells
+adjacent to cells with a higher or lower polynomial degree. This is,
+in fact, not much more than the fraction of constrained degrees of
+freedom in non-$hp$ mode, but the difference is that each constrained
+hanging node is constrained not only against the two adjacent degrees
+of freedom, but is constrained against many more degrees of freedom.
 
 In previous programs, for example in step-6, we have dealt with eliminating
 these constrained degrees of freedom by first building an object of type
diff --git a/deal.II/examples/step-27/doc/results.dox b/deal.II/examples/step-27/doc/results.dox
index 957c48b172..04d7d28d22 100644
--- a/deal.II/examples/step-27/doc/results.dox
+++ b/deal.II/examples/step-27/doc/results.dox
@@ -1,6 +1,13 @@
 <a name="Results"></a>
 <h1>Results</h1>
 
+In this section, we discuss a few results produced from running the
+current tutorial program. More results, in particular the extension to
+3d calculations and determining how much compute time the individual
+components of the program take, are given in the @ref hp_paper .
+
+When run, this is what the program produces:
+
 <code>
 <pre>
 examples/step-27> make run
@@ -31,3 +38,15 @@ Cycle 5:
    Number of constraints       : 6196
 </pre>
 </code>
+
+The first thing we learn from this is that the number of constrained
+degrees of freedom is on the order of 20-25% of the total number of
+degrees of freedom, at least on the later grids when we have elements
+of relatively high order. This is, in fact, on the same order of
+magnitude as for non-$hp$ discretizations. For example, in the last
+step of the @ref step_6 "step-6" program, we have 18401 degrees of
+freedom, 4104 of which are constrained. The difference is that in the
+latter program, each constrained hanging node is constrained against
+only the two adjacent degrees of freedom, whereas in the $hp$ case,
+constrained nodes are constrained against many more degrees of
+freedom. 
-- 
2.39.5