More results for the Laplace eqn on circle, unfitted with Monte-Carlo method.
Various narrow band widths:
1h strip
h Nodes Time | L2(Gamma) H1(Gamma) Area*St.dev
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0.1000 181 0:0:1s | 1.33e-03 7.30e-02 5.11e-03
0.0500 357 0:0:5s | 1.92e-04 2.79 2.03e-02 1.84 1.26e-03 2.02
0.0250 709 0:0:6s | 2.41e-05 2.99 5.29e-03 1.94 1.68e-04 2.90
0.0125 1381 0:0:14s | 2.97e-06 3.02 1.35e-03 1.97 3.11e-05 2.44
0.0063 2817 0:4:17s | 3.73e-07 2.99 3.38e-04 2.00 3.94e-06 2.98
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same refinement, several monte-carlo runs:
0.0250 709 0:0:6s | 2.98e-05 5.30e-03 1.61e-04
0.0250 709 0:0:6s | 2.73e-05 0.12 5.30e-03 0.00 1.60e-04 0.01
0.0250 709 0:0:6s | 2.60e-05 0.07 5.29e-03 0.00 1.64e-04 -0.03
0.0250 709 0:0:6s | 2.32e-05 0.16 5.29e-03 -0.00 1.63e-04 0.01
0.0250 709 0:0:6s | 2.31e-05 0.00 5.29e-03 0.00 1.64e-04 -0.01
0.0250 709 0:0:6s | 2.32e-05 -0.00 5.29e-03 -0.00 1.64e-04 0.00
0.0250 709 0:0:6s | 2.35e-05 -0.02 5.29e-03 0.00 1.65e-04 -0.01
0.0250 709 0:0:6s | 2.48e-05 -0.08 5.28e-03 0.00 1.67e-04 -0.02
0.0250 709 0:0:6s | 2.63e-05 -0.08 5.30e-03 -0.00 1.65e-04 0.02
0.0250 709 0:0:6s | 2.43e-05 0.11 5.30e-03 0.00 1.64e-04 0.01
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Same setup with sub-triangulations:
h Nodes Time | L2(Gamma) H1(Gamma) Area*St.dev
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0.1000 181 0:0:1s | 1.30e-03 7.36e-02 0.00e+00
0.0500 357 0:0:7s | 1.75e-04 2.89 2.03e-02 1.86 0.00e+00 NaN
0.0250 709 0:0:16s | 2.31e-05 2.92 5.29e-03 1.94 0.00e+00 NaN
0.0125 1381 0:0:51s | 2.96e-06 2.96 1.35e-03 1.97 0.00e+00 NaN
0.0063 2817 0:3:16s | 3.73e-07 2.99 3.38e-04 2.00 0.00e+00 NaN
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3h strip
h Nodes Time | L2(Gamma) H1(Gamma) Area*St.dev
---------------------------------------------------------------------------------------
0.1000 353 0:0:6s | 1.43e-03 8.17e-02 5.38e-03
0.0500 697 0:0:6s | 1.93e-04 2.89 2.25e-02 1.86 1.39e-03 1.95
0.0250 1361 0:0:7s | 2.56e-05 2.91 5.84e-03 1.95 1.45e-04 3.27
0.0125 2717 0:0:16s | 3.28e-06 2.96 1.49e-03 1.97 2.20e-05 2.71
0.0063 5457 0:4:34s | 4.16e-07 2.98 3.73e-04 2.00 3.37e-06 2.71
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same refinement, several monte-carlo runs:
0.0250 1361 0:0:8s | 2.55e-05 5.84e-03 1.48e-04
0.0250 1361 0:0:8s | 2.56e-05 -0.00 5.84e-03 -0.00 1.52e-04 -0.04
0.0250 1361 0:0:7s | 2.55e-05 0.00 5.84e-03 0.00 1.45e-04 0.06
0.0250 1361 0:0:8s | 2.57e-05 -0.01 5.84e-03 -0.00 1.45e-04 -0.00
0.0250 1361 0:0:7s | 2.56e-05 0.01 5.84e-03 0.00 1.50e-04 -0.05
0.0250 1361 0:0:7s | 2.56e-05 -0.00 5.84e-03 -0.00 1.49e-04 0.01
0.0250 1361 0:0:7s | 2.56e-05 0.00 5.84e-03 0.00 1.48e-04 0.00
0.0250 1361 0:0:7s | 2.56e-05 -0.00 5.84e-03 0.00 1.49e-04 -0.00
0.0250 1361 0:0:7s | 2.55e-05 0.00 5.84e-03 -0.00 1.49e-04 -0.00
0.0250 1361 0:0:7s | 2.55e-05 0.00 5.84e-03 0.00 1.50e-04 -0.01
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5h
h Nodes Time | L2(Gamma) H1(Gamma) Area*St.dev
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0.1000 501 0:0:6s | 1.58e-03 8.17e-02 9.69e-03
0.0500 1013 0:0:6s | 2.06e-04 2.94 2.25e-02 1.86 2.19e-03 2.14
0.0250 1997 0:0:8s | 2.56e-05 3.01 5.84e-03 1.95 3.34e-04 2.71
0.0125 3989 0:0:17s | 3.29e-06 2.96 1.49e-03 1.97 4.08e-05 3.03
0.0063 7941 0:4:33s | 4.14e-07 2.99 3.73e-04 2.00 5.01e-06 3.03
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