From 39c120a9cca8769e451ec4eefbc81c9facb8f872 Mon Sep 17 00:00:00 2001 From: wolf Date: Wed, 22 Mar 2000 15:33:49 +0000 Subject: [PATCH] Finish. git-svn-id: https://svn.dealii.org/trunk@2616 0785d39b-7218-0410-832d-ea1e28bc413d --- .../step-7.data/results.html | 238 +++++++++++++++++- .../step-7.data/solution-3d.jpg | Bin 0 -> 17524 bytes 2 files changed, 237 insertions(+), 1 deletion(-) create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-7.data/solution-3d.jpg 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 @@

Results

-Still to be written. +The program generates two kinds of output. The first are the output +files solution-adaptive-q1.gmv, +solution-global-q1.gmv, and +solution-global-q2.gmv. We show the latter in a 3d view +here:

+ +

+ solution +

+ + +

+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: +

+ + +
+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
+
+
+ + +

+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 H1 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 L2 norm. +

+ + +

+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: +

+ + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+n cells

H1-errorL2-error
042.445e+00-1.433e+00--
1161.168e+001.077.912e-0218.114.18
2642.511e-012.227.755e-0310.203.35
32566.235e-022.019.969e-047.782.96
410241.571e-021.991.265e-047.882.98
540963.937e-032.001.587e-057.972.99
6163849.847e-042.001.986e-067.993.00
+
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