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 d055bf84a5892cf48a5d2e10c6d2edf0be34fb55..a8eb4511d8b0f5ca4597fd687f6ad6c80f70e5d8 100644 (file)
--- 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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