From 95373d167cabaa9bcfdc83e8352c7c22825e3d34 Mon Sep 17 00:00:00 2001
From: wolf
Refinement cycle: 0
Number of degrees of freedom=72
- Point x-derivative=-0.287759
+ Point x-derivative=-0.0719397
Estimated error=-0.0126173
Refinement cycle: 1
Number of degrees of freedom=61
- Point x-derivative=-0.283182
+ Point x-derivative=-0.0707956
Estimated error=-0.00774316
Refinement cycle: 2
Number of degrees of freedom=131
- Point x-derivative=-0.227468
+ Point x-derivative=-0.0568671
Estimated error=-0.00313426
Refinement cycle: 3
Number of degrees of freedom=247
- Point x-derivative=-0.212132
+ Point x-derivative=-0.053033
Estimated error=-0.00136114
Refinement cycle: 4
Number of degrees of freedom=541
- Point x-derivative=-0.210584
+ Point x-derivative=-0.0526461
Estimated error=-0.000555479
Refinement cycle: 5
Number of degrees of freedom=1286
- Point x-derivative=-0.210758
+ Point x-derivative=-0.0526896
Estimated error=-0.0002261
Refinement cycle: 6
Number of degrees of freedom=2924
- Point x-derivative=-0.211001
+ Point x-derivative=-0.0527503
Estimated error=-9.38035e-05
Refinement cycle: 7
Number of degrees of freedom=6578
- Point x-derivative=-0.211151
+ Point x-derivative=-0.0527877
Estimated error=-3.94139e-05
Refinement cycle: 8
Number of degrees of freedom=14780
- Point x-derivative=-0.211219
+ Point x-derivative=-0.0528047
Estimated error=-1.85456e-05
Refinement cycle: 9
Number of degrees of freedom=31438
- Point x-derivative=-0.211258
+ Point x-derivative=-0.0528145
Then, it is interesting to compare actually computed values of the quantity of interest (i.e. the x-derivative of the solution at one -point) with a reference value of -0.211289... plus or minus -0.000002. We get this reference value by computing on finer grid after +point) with a reference value of -0.0528223... plus or minus +0.0000005. We get this reference value by computing on finer grid after some more mesh refinements, with approximately 130,000 cells. Recall that if the error is O(1/N) in the optimal case, then taking a mesh with ten times more cells gives us one additional digit -- 2.39.5