]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
More for step-14.
authorwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 30 Apr 2002 11:59:16 +0000 (11:59 +0000)
committerwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 30 Apr 2002 11:59:16 +0000 (11:59 +0000)
git-svn-id: https://svn.dealii.org/trunk@5769 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/point_value/error-comparison.gif
deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/results.html

index 0de02cd27ba330d99faef08a5a07f4d5a2ef9145..f3da4a3c66e7887f4bfa8201bb1460686b5e17c8 100644 (file)
Binary files a/deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/point_value/error-comparison.gif and b/deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/point_value/error-comparison.gif differ
index 7729ae91d77d7745a1c975793f9b93985a07d79f..ebb5ee88bbbf03cbc37a11feb86120adc55cc9ac 100644 (file)
@@ -197,8 +197,33 @@ the dual problem, and for evaluating the error representation), it is
 worth while asking whether that effort was successful. To this end, we
 first compare the achieved error levels for different mesh refinement
 criteria. To generate this data, simply change the value of the mesh
-refinement criterion variable in the main program. The results are thus:
-TODO
+refinement criterion variable in the main program. The results are
+thus (for the weight in the Kelly indicator, we have chosen the
+function <em>1/(r<sup>2</sup>+0.1<sup>2</sup>)</em>, where <em>r</em>
+is the distance to the evaluation point):
+</p>
+<p align="center">
+ <a href="step-14.data/point_value/error-comparison.gif"
+  target="_top"><img alt="Error comparison"
+  src="step-14.data/point_value/error-comparison.gif">
+ </img></a>
+</p>
+
+<p>
+Checking these numbers, we see that for global refinement, the error
+is proportional to <em>O(1/(sqrt(N) log(N)))</em>, and for the dual
+estimator <em>O(1/N)</em>. Generally speaking, we see that the dual
+weighted error estimator is better than the other refinement
+indicators, at least when compared with those that have a similarly
+regular behavior. The Kelly indicator produces smaller errors, but
+jumps about the picture rather irregularly, with the error also
+changing signs sometimes. Therefore, its behavior does not allow to
+extrapolate the results to larger values of N. Furthermore, if we
+trust the error estimates of the dual weighted error estimator, the
+results can be improved by adding the estimated error to the computed
+values. In terms of reliability, the weighted estimator is thus better
+than the Kelly indicator, although the latter sometimes produces
+smaller errors.
 </p>
 
 

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