<h1>Results</h1>
-The output of this program consist of the console output, the eps
-files including the grids, and the solutions given in gnuplot format.
-@code
-Cycle 0:
- Number of active cells: 64
- Number of degrees of freedom: 256
-Time of assemble_system1: 0.05
-Time of assemble_system2: 0.04
-solution1 and solution2 coincide.
-Writing grid to <grid-0.eps>...
-Writing solution to <sol-0.gnuplot>...
-
-Cycle 1:
- Number of active cells: 112
- Number of degrees of freedom: 448
-Time of assemble_system1: 0.09
-Time of assemble_system2: 0.07
-solution1 and solution2 coincide.
-Writing grid to <grid-1.eps>...
-Writing solution to <sol-1.gnuplot>...
-
-Cycle 2:
- Number of active cells: 214
- Number of degrees of freedom: 856
-Time of assemble_system1: 0.17
-Time of assemble_system2: 0.14
-solution1 and solution2 coincide.
-Writing grid to <grid-2.eps>...
-Writing solution to <sol-2.gnuplot>...
-
-Cycle 3:
- Number of active cells: 415
- Number of degrees of freedom: 1660
-Time of assemble_system1: 0.32
-Time of assemble_system2: 0.28
-solution1 and solution2 coincide.
-Writing grid to <grid-3.eps>...
-Writing solution to <sol-3.gnuplot>...
-
-Cycle 4:
- Number of active cells: 796
- Number of degrees of freedom: 3184
-Time of assemble_system1: 0.62
-Time of assemble_system2: 0.52
-solution1 and solution2 coincide.
-Writing grid to <grid-4.eps>...
-Writing solution to <sol-4.gnuplot>...
-
-Cycle 5:
- Number of active cells: 1561
- Number of degrees of freedom: 6244
-Time of assemble_system1: 1.23
-Time of assemble_system2: 1.03
-solution1 and solution2 coincide.
-Writing grid to <grid-5.eps>...
-Writing solution to <sol-5.gnuplot>...
-@endcode
-
-We see that, as expected, on each refinement step the two solutions
-coincide. The difference measured in time of treating each face only
-once (second version of the DG method) in comparison with treating
-each face twice within a nested loop over all cells and all faces of
-each cell (first version), is much less than one might have
-expected. The gain is less than 20% on the last few refinement steps.
-
-
- First we show the solutions on the initial mesh, the mesh after two
-and after five adaptive refinement steps.
-
-@image html step-12.sol-0.png
-@image html step-12.sol-2.png
-@image html step-12.sol-5.png
-
-
-Then we show the final grid (after 5 refinement steps) and the solution again,
-this time with a nicer 3d rendering (obtained using the DataOutBase::write_vtk
-function and the VTK-based VisIt visualization program) that better shows the
-sharpness of the jump on the refined mesh and the over- and undershoots of the
-solution along the interface:
-
-@image html step-12.grid-5.png
-@image html step-12.3d-solution.png
-
-
-And finally we show a plot of a 3d computation.
-
-@image html step-12.sol-5-3d.png
-