From: wolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Wed, 22 Mar 2000 15:33:49 +0000 (+0000)
Subject: Finish.
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=39c120a9cca8769e451ec4eefbc81c9facb8f872;p=dealii-svn.git

Finish.


git-svn-id: https://svn.dealii.org/trunk@2616 0785d39b-7218-0410-832d-ea1e28bc413d
---

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-7.data/results.html b/deal.II/doc/tutorial/chapter-2.step-by-step/step-7.data/results.html
index d055bf84a5..a8eb4511d8 100644
--- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-7.data/results.html
+++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-7.data/results.html
@@ -2,5 +2,241 @@
 <h1>Results</h1>
 
 <p>
-Still to be written.
+The program generates two kinds of output. The first are the output
+files <code>solution-adaptive-q1.gmv</code>,
+<code>solution-global-q1.gmv</code>, and
+<code>solution-global-q2.gmv</code>. We show the latter in a 3d view
+here: 
 </p>
+
+<p align="center">
+  <img src="step-7.data/solution-3d.jpg" alt="solution" width="75%">
+</p>
+
+
+<p>
+The second are the various kinds of tables. Some are shown in the
+output written to the screen while the program runs, which we first
+display:
+</p>
+
+<code>
+<pre>
+Solving with Q1 elements, adaptive refinement
+=============================================
+
+Cycle 0:
+   Number of active cells:       4
+   Number of degrees of freedom: 9
+Cycle 1:
+   Number of active cells:       13
+   Number of degrees of freedom: 22
+Cycle 2:
+   Number of active cells:       31
+   Number of degrees of freedom: 46
+Cycle 3:
+   Number of active cells:       64
+   Number of degrees of freedom: 87
+Cycle 4:
+   Number of active cells:       127
+   Number of degrees of freedom: 160
+Cycle 5:
+   Number of active cells:       244
+   Number of degrees of freedom: 297
+Cycle 6:
+   Number of active cells:       466
+   Number of degrees of freedom: 543
+
+cycle  	cells  	dofs   	L2             	H1             	Linfty         	
+0	4	9	1.198e+00	2.732e+00	1.383e+00
+1	13	22	8.795e-02	1.193e+00	1.816e-01
+2	31	46	8.147e-02	1.167e+00	1.654e-01
+3	64	87	7.702e-02	1.077e+00	1.310e-01
+4	127	160	4.643e-02	7.988e-01	6.745e-02
+5	244	297	2.470e-02	5.568e-01	3.668e-02
+6	466	543	1.622e-02	4.107e-01	2.966e-02
+
+
+n cells        	H1             	L2             	
+0	4	2.732e+00	1.198e+00
+1	13	1.193e+00	8.795e-02
+2	31	1.167e+00	8.147e-02
+3	64	1.077e+00	7.702e-02
+4	127	7.988e-01	4.643e-02
+5	244	5.568e-01	2.470e-02
+6	466	4.107e-01	1.622e-02
+
+
+Solving with Q1 elements, global refinement
+===========================================
+
+Cycle 0:
+   Number of active cells:       4
+   Number of degrees of freedom: 9
+Cycle 1:
+   Number of active cells:       16
+   Number of degrees of freedom: 25
+Cycle 2:
+   Number of active cells:       64
+   Number of degrees of freedom: 81
+Cycle 3:
+   Number of active cells:       256
+   Number of degrees of freedom: 289
+Cycle 4:
+   Number of active cells:       1024
+   Number of degrees of freedom: 1089
+Cycle 5:
+   Number of active cells:       4096
+   Number of degrees of freedom: 4225
+Cycle 6:
+   Number of active cells:       16384
+   Number of degrees of freedom: 16641
+
+cycle  	cells  	dofs   	L2             	H1             	Linfty         	
+0	4	9	1.198e+00	2.732e+00	1.383e+00
+1	16	25	8.281e-02	1.190e+00	1.808e-01
+2	64	81	8.142e-02	1.129e+00	1.294e-01
+3	256	289	2.113e-02	5.828e-01	4.917e-02
+4	1024	1089	5.319e-03	2.934e-01	1.359e-02
+5	4096	4225	1.332e-03	1.469e-01	3.482e-03
+6	16384	16641	3.332e-04	7.350e-02	8.758e-04
+
+
+n cells        	H1                     	L2                             	
+0	4	2.732e+00	-	1.198e+00	-	-
+1	16	1.190e+00	1.20	8.281e-02	14.47	3.86
+2	64	1.129e+00	0.08	8.142e-02	1.02	0.02
+3	256	5.828e-01	0.95	2.113e-02	3.85	1.95
+4	1024	2.934e-01	0.99	5.319e-03	3.97	1.99
+5	4096	1.469e-01	1.00	1.332e-03	3.99	2.00
+6	16384	7.350e-02	1.00	3.332e-04	4.00	2.00
+
+
+Solving with Q2 elements, global refinement
+===========================================
+
+Cycle 0:
+   Number of active cells:       4
+   Number of degrees of freedom: 25
+Cycle 1:
+   Number of active cells:       16
+   Number of degrees of freedom: 81
+Cycle 2:
+   Number of active cells:       64
+   Number of degrees of freedom: 289
+Cycle 3:
+   Number of active cells:       256
+   Number of degrees of freedom: 1089
+Cycle 4:
+   Number of active cells:       1024
+   Number of degrees of freedom: 4225
+Cycle 5:
+   Number of active cells:       4096
+   Number of degrees of freedom: 16641
+Cycle 6:
+   Number of active cells:       16384
+   Number of degrees of freedom: 66049
+
+cycle  	cells  	dofs   	L2             	H1             	Linfty         	
+0	4	25	1.433e+00	2.445e+00	1.286e+00
+1	16	81	7.912e-02	1.168e+00	1.728e-01
+2	64	289	7.755e-03	2.511e-01	1.991e-02
+3	256	1089	9.969e-04	6.235e-02	2.764e-03
+4	1024	4225	1.265e-04	1.571e-02	3.527e-04
+5	4096	16641	1.587e-05	3.937e-03	4.343e-05
+6	16384	66049	1.986e-06	9.847e-04	5.402e-06
+
+
+n cells        	H1                     	L2                             	
+0	4	2.445e+00	-	1.433e+00	-	-
+1	16	1.168e+00	1.07	7.912e-02	18.11	4.18
+2	64	2.511e-01	2.22	7.755e-03	10.20	3.35
+3	256	6.235e-02	2.01	9.969e-04	7.78	2.96
+4	1024	1.571e-02	1.99	1.265e-04	7.88	2.98
+5	4096	3.937e-03	2.00	1.587e-05	7.97	2.99
+6	16384	9.847e-04	2.00	1.986e-06	7.99	3.00
+</pre>
+</code>
+
+
+<p>
+One can see the error reduction upon grid refinement, and for the
+cases where global refinement was performed, also the convergence
+rates can be seen. The convergence rates in the H<sup>1</sup> norm of
+1 and 2 for Q1 and Q2 elements, respectively, can clearly be seen, as
+are the rates of 2 and 3 in the L<sub>2</sub> norm.
+</p>
+
+
+<p>
+Finally, the program generated various LaTeX tables. We show here
+the convergence table of the Q2 element with global refinement, after
+converting the format to HTML:
+</p>
+
+
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
+<TR><TD ALIGN="CENTER" COLSPAN=2><P>
+n cells</TD>
+<TD ALIGN="CENTER" COLSPAN=2><I>H</I><SUP>1</SUP>-error</TD>
+<TD ALIGN="CENTER" COLSPAN=3><I>L</I><SUP>2</SUP>-error</TD>
+</TR>
+<TR><TD ALIGN="CENTER">0</TD>
+<TD ALIGN="RIGHT">4</TD>
+<TD ALIGN="CENTER">2.445e+00</TD>
+<TD ALIGN="CENTER">-</TD>
+<TD ALIGN="CENTER">1.433e+00</TD>
+<TD ALIGN="CENTER">-</TD>
+<TD ALIGN="CENTER">-</TD>
+</TR>
+<TR><TD ALIGN="CENTER">1</TD>
+<TD ALIGN="RIGHT">16</TD>
+<TD ALIGN="CENTER">1.168e+00</TD>
+<TD ALIGN="CENTER">1.07</TD>
+<TD ALIGN="CENTER">7.912e-02</TD>
+<TD ALIGN="CENTER">18.11</TD>
+<TD ALIGN="CENTER">4.18</TD>
+</TR>
+<TR><TD ALIGN="CENTER">2</TD>
+<TD ALIGN="RIGHT">64</TD>
+<TD ALIGN="CENTER">2.511e-01</TD>
+<TD ALIGN="CENTER">2.22</TD>
+<TD ALIGN="CENTER">7.755e-03</TD>
+<TD ALIGN="CENTER">10.20</TD>
+<TD ALIGN="CENTER">3.35</TD>
+</TR>
+<TR><TD ALIGN="CENTER">3</TD>
+<TD ALIGN="RIGHT">256</TD>
+<TD ALIGN="CENTER">6.235e-02</TD>
+<TD ALIGN="CENTER">2.01</TD>
+<TD ALIGN="CENTER">9.969e-04</TD>
+<TD ALIGN="CENTER">7.78</TD>
+<TD ALIGN="CENTER">2.96</TD>
+</TR>
+<TR><TD ALIGN="CENTER">4</TD>
+<TD ALIGN="RIGHT">1024</TD>
+<TD ALIGN="CENTER">1.571e-02</TD>
+<TD ALIGN="CENTER">1.99</TD>
+<TD ALIGN="CENTER">1.265e-04</TD>
+<TD ALIGN="CENTER">7.88</TD>
+<TD ALIGN="CENTER">2.98</TD>
+</TR>
+<TR><TD ALIGN="CENTER">5</TD>
+<TD ALIGN="RIGHT">4096</TD>
+<TD ALIGN="CENTER">3.937e-03</TD>
+<TD ALIGN="CENTER">2.00</TD>
+<TD ALIGN="CENTER">1.587e-05</TD>
+<TD ALIGN="CENTER">7.97</TD>
+<TD ALIGN="CENTER">2.99</TD>
+</TR>
+<TR><TD ALIGN="CENTER">6</TD>
+<TD ALIGN="RIGHT">16384</TD>
+<TD ALIGN="CENTER">9.847e-04</TD>
+<TD ALIGN="CENTER">2.00</TD>
+<TD ALIGN="CENTER">1.986e-06</TD>
+<TD ALIGN="CENTER">7.99</TD>
+<TD ALIGN="CENTER">3.00</TD>
+</TR>
+</TABLE></DIV>
+<BR>
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