by simply letting it run, unmodified:
@code
Refinement cycle: 0
- Number of degrees of freedom=72
- Point value=0.03243
- Estimated error=0.000702385
+ Number of degrees of freedom: 72
+ Point value: 0.03243
+ Estimated error: 0.000702385
Refinement cycle: 1
- Number of degrees of freedom=67
- Point value=0.0324827
- Estimated error=0.000888953
+ Number of degrees of freedom: 67
+ Point value: 0.0324827
+ Estimated error: 0.000888953
Refinement cycle: 2
- Number of degrees of freedom=130
- Point value=0.0329619
- Estimated error=0.000454606
+ Number of degrees of freedom: 130
+ Point value: 0.0329619
+ Estimated error: 0.000454606
Refinement cycle: 3
- Number of degrees of freedom=307
- Point value=0.0331934
- Estimated error=0.000241254
+ Number of degrees of freedom: 307
+ Point value: 0.0331934
+ Estimated error: 0.000241254
Refinement cycle: 4
- Number of degrees of freedom=718
- Point value=0.0333675
- Estimated error=7.4912e-05
+ Number of degrees of freedom: 718
+ Point value: 0.0333675
+ Estimated error: 7.4912e-05
Refinement cycle: 5
- Number of degrees of freedom=1665
- Point value=0.0334083
- Estimated error=3.69111e-05
+ Number of degrees of freedom: 1665
+ Point value: 0.0334083
+ Estimated error: 3.69111e-05
Refinement cycle: 6
- Number of degrees of freedom=3975
- Point value=0.033431
- Estimated error=1.54218e-05
+ Number of degrees of freedom: 3975
+ Point value: 0.033431
+ Estimated error: 1.54218e-05
Refinement cycle: 7
- Number of degrees of freedom=8934
- Point value=0.0334406
- Estimated error=6.28359e-06
+ Number of degrees of freedom: 8934
+ Point value: 0.0334406
+ Estimated error: 6.28359e-06
Refinement cycle: 8
- Number of degrees of freedom=21799
- Point value=0.0334444
+ Number of degrees of freedom: 21799
+ Point value: 0.0334444
@endcode
<code>PointXDerivativeEvaluation</code>, and let the program run:
@code
Refinement cycle: 0
- Number of degrees of freedom=72
- Point x-derivative=-0.0719397
- Estimated error=-0.0126173
+ Number of degrees of freedom: 72
+ Point x-derivative: -0.0719397
+ Estimated error: -0.0126173
Refinement cycle: 1
- Number of degrees of freedom=61
- Point x-derivative=-0.0707956
- Estimated error=-0.00774316
+ Number of degrees of freedom: 61
+ Point x-derivative: -0.0707956
+ Estimated error: -0.00774316
Refinement cycle: 2
- Number of degrees of freedom=131
- Point x-derivative=-0.0568671
- Estimated error=-0.00313426
+ Number of degrees of freedom: 131
+ Point x-derivative: -0.0568671
+ Estimated error: -0.00313426
Refinement cycle: 3
- Number of degrees of freedom=247
- Point x-derivative=-0.053033
- Estimated error=-0.00136114
+ Number of degrees of freedom: 247
+ Point x-derivative: -0.053033
+ Estimated error: -0.00136114
Refinement cycle: 4
- Number of degrees of freedom=532
- Point x-derivative=-0.0526429
- Estimated error=-0.000558868
+ Number of degrees of freedom: 532
+ Point x-derivative: -0.0526429
+ Estimated error: -0.000558868
Refinement cycle: 5
- Number of degrees of freedom=1267
- Point x-derivative=-0.0526955
- Estimated error=-0.000220116
+ Number of degrees of freedom: 1267
+ Point x-derivative: -0.0526955
+ Estimated error: -0.000220116
Refinement cycle: 6
- Number of degrees of freedom=2864
- Point x-derivative=-0.0527495
- Estimated error=-9.46731e-05
+ Number of degrees of freedom: 2864
+ Point x-derivative: -0.0527495
+ Estimated error: -9.46731e-05
Refinement cycle: 7
- Number of degrees of freedom=6409
- Point x-derivative=-0.052785
- Estimated error=-4.21543e-05
+ Number of degrees of freedom: 6409
+ Point x-derivative: -0.052785
+ Estimated error: -4.21543e-05
Refinement cycle: 8
- Number of degrees of freedom=14183
- Point x-derivative=-0.0528028
- Estimated error=-2.04241e-05
+ Number of degrees of freedom: 14183
+ Point x-derivative: -0.0528028
+ Estimated error: -2.04241e-05
Refinement cycle: 9
- Number of degrees of freedom=29902
- Point x-derivative=-0.052814
+ Number of degrees of freedom: 29902
+ Point x-derivative: -0.052814
@endcode
Number of degrees of freedom: 1089
DEAL:cg::Starting value 0.121094
DEAL:cg::Convergence step 36 value 7.07761e-08
+Output written to solution.vtk
@endcode
-The first two lines is what we wrote to <code>std::cout</code>. The last
+The first two lines is what we wrote to <code>std::cout</code>. The next
two lines were generated by the CG solver because we called
`deallog.depth_console(2);` in the `main()` function -- see
the lengthy discussion there. These two lines prefixed by `DEAL:cg:` state
norm of the right hand side vector, and there is indeed more than a
factor of $10^{-6}$ between the two values shown.
-Apart from the output shown above, the program generated the file
+The last line is the output we generated at the bottom of the
+`output_results()` function. The program also generated the file
<code>solution.vtk</code>, which is in the VTK format that is widely
used by many visualization programs today -- including the two
heavy-weights <a href="https://www.llnl.gov/visit">VisIt</a> and