Open Access
Table 6
-error on 8 layer-adapted meshes for Example 2, where 
| k | N | S-mesh | BS-mesh | mBS-mesh | VS-mesh | pS-mesh | B-mesh | mVB-mesh | RS-mesh | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| L²-error |
|
L²-error |
|
L²-error |
|
L²-error |
|
L²-error |
|
L²-error |
|
L²-error |
|
L²-error |
|
||
| 1 | 4 | 8.64E-04 | ― | 5.90E-04 | ― | 6.04E-04 | ― | 6.04E-04 | ― | 6.79E-04 | ― | 1.31E-03 | ― | 1.31E-03 | ― | 7.32E-04 | ― |
| 8 | 5.46E-04 | 1.59 | 2.29E-04 | 1.37 | 2.35E-04 | 1.36 | 2.35E-04 | 1.36 | 3.16E-04 | 1.11 | 3.28E-04 | 1.99 | 4.03E-04 | 1.70 | 4.59E-04 | 0.67 | |
| 16 | 2.70E-04 | 1.73 | 7.16E-05 | 1.68 | 7.58E-05 | 1.63 | 7.58E-05 | 1.63 | 1.16E-04 | 1.45 | 8.49E-05 | 1.95 | 1.12E-04 | 1.85 | 2.08E-04 | 1.14 | |
| 32 | 1.14E-04 | 1.84 | 2.02E-05 | 1.82 | 2.23E-05 | 1.76 | 2.23E-05 | 1.76 | 3.83E-05 | 1.60 | 2.20E-05 | 1.95 | 2.98E-05 | 1.90 | 9.06E-05 | 1.20 | |
| 64 | 4.28E-05 | 1.91 | 5.41E-06 | 1.90 | 6.21E-06 | 1.84 | 6.21E-06 | 1.84 | 1.19E-05 | 1.69 | 5.63E-06 | 1.96 | 7.74E-06 | 1.95 | 3.80E-05 | 1.25 | |
| 128 | 1.50E-05 | 1.95 | 1.40E-06 | 1.95 | 1.67E-06 | 1.89 | 1.67E-06 | 1.89 | 3.53E-06 | 1.75 | 1.43E-06 | 1.98 | 1.98E-06 | 1.97 | 1.56E-05 | 1.29 | |
| 256 | 4.95E-06 | 1.97 | 3.58E-07 | 1.97 | 4.41E-07 | 1.92 | 4.41E-07 | 1.92 | 1.02E-06 | 1.79 | 3.61E-07 | 1.98 | 4.99E-07 | 1.98 | 6.29E-06 | 1.31 | |
| 512 | 1.58E-06 | 1.99 | 9.05E-08 | 1.98 | 1.15E-07 | 1.94 | 1.15E-07 | 1.94 | 2.88E-07 | 1.82 | 9.09E-08 | 1.99 | 1.25E-07 | 1.99 | 2.53E-06 | 1.32 | |
| 1 024 | 4.90E-07 | 1.99 | 2.28E-08 | 1.99 | 2.95E-08 | 1.96 | 2.95E-08 | 1.96 | 8.02E-08 | 1.84 | 2.28E-08 | 1.99 | 3.15E-08 | 2.00 | 1.01E-06 | 1.32 | |
| 2 | 4 | 2.91E-04 | ― | 1.51E-04 | ― | 1.63E-04 | ― | 1.63E-04 | ― | 2.09E-04 | ― | 4.90E-04 | ― | 4.93E-04 | ― | 2.39E-04 | ― |
| 8 | 1.45E-04 | 2.41 | 3.36E-05 | 2.17 | 3.61E-05 | 2.18 | 3.61E-05 | 2.18 | 5.91E-05 | 1.82 | 5.83E-05 | 3.07 | 8.30E-05 | 2.57 | 1.09E-04 | 1.13 | |
| 16 | 5.01E-05 | 2.63 | 5.57E-06 | 2.59 | 6.25E-06 | 2.53 | 6.25E-06 | 2.53 | 1.25E-05 | 2.24 | 7.25E-06 | 3.01 | 1.13E-05 | 2.87 | 3.23E-05 | 1.75 | |
| 32 | 1.35E-05 | 2.80 | 8.06E-07 | 2.79 | 9.65E-07 | 2.69 | 9.65E-07 | 2.69 | 2.31E-06 | 2.44 | 9.16E-07 | 2.98 | 1.50E-06 | 2.91 | 8.95E-06 | 1.85 | |
| 64 | 3.06E-06 | 2.90 | 1.09E-07 | 2.89 | 1.39E-07 | 2.79 | 1.39E-07 | 2.79 | 3.92E-07 | 2.56 | 1.16E-07 | 2.98 | 1.94E-07 | 2.95 | 2.38E-06 | 1.91 | |
| 128 | 6.25E-07 | 2.95 | 1.42E-08 | 2.94 | 1.92E-08 | 2.86 | 1.92E-08 | 2.86 | 6.27E-08 | 2.64 | 1.46E-08 | 2.99 | 2.47E-08 | 2.97 | 6.14E-07 | 1.95 | |
| 256 | 1.18E-07 | 2.97 | 1.82E-09 | 2.97 | 2.58E-09 | 2.89 | 2.58E-09 | 2.89 | 9.65E-09 | 2.70 | 1.84E-09 | 2.99 | 3.12E-09 | 2.99 | 1.56E-07 | 1.97 | |
| 512 | 2.12E-08 | 2.99 | 2.30E-10 | 2.98 | 3.41E-10 | 2.92 | 3.41E-10 | 2.92 | 1.45E-09 | 2.74 | 2.32E-10 | 2.99 | 3.91E-10 | 2.99 | 3.96E-08 | 1.98 | |
| 1 024 | 3.65E-09 | 2.99 | 2.89E-11 | 2.99 | 4.46E-11 | 2.94 | 4.46E-11 | 2.94 | 2.12E-10 | 2.77 | 2.90E-11 | 3.00 | 4.90E-11 | 3.00 | 9.95E-09 | 1.99 | |
| 3 | 4 | 9.92E-05 | ― | 3.87E-05 | ― | 4.50E-05 | ― | 4.50E-05 | ― | 6.54E-05 | ― | 1.70E-04 | ― | 1.81E-04 | ― | 7.88E-05 | ― |
| 8 | 3.97E-05 | 3.18 | 4.99E-06 | 2.96 | 5.68E-06 | 2.99 | 5.68E-06 | 2.99 | 1.13E-05 | 2.53 | 1.01E-05 | 4.08 | 1.75E-05 | 3.37 | 2.66E-05 | 1.57 | |
| 16 | 9.68E-06 | 3.48 | 4.40E-07 | 3.50 | 5.33E-07 | 3.41 | 5.33E-07 | 3.41 | 1.41E-06 | 3.01 | 6.19E-07 | 4.02 | 1.19E-06 | 3.88 | 5.25E-06 | 2.34 | |
| 32 | 1.68E-06 | 3.73 | 3.28E-08 | 3.75 | 4.33E-08 | 3.62 | 4.33E-08 | 3.62 | 1.45E-07 | 3.28 | 3.87E-08 | 4.00 | 7.84E-08 | 3.92 | 9.20E-07 | 2.51 | |
| 64 | 2.33E-07 | 3.87 | 2.24E-09 | 3.87 | 3.23E-09 | 3.74 | 3.23E-09 | 3.74 | 1.35E-08 | 3.43 | 2.44E-09 | 3.99 | 5.05E-09 | 3.95 | 1.55E-07 | 2.57 | |
| 128 | 2.78E-08 | 3.94 | 1.47E-10 | 3.93 | 2.29E-10 | 3.82 | 2.29E-10 | 3.82 | 1.16E-09 | 3.53 | 1.53E-10 | 3.99 | 3.21E-10 | 3.98 | 2.53E-08 | 2.61 | |
| 256 | 3.01E-09 | 3.97 | 9.44E-12 | 3.96 | 1.58E-11 | 3.86 | 1.58E-11 | 3.86 | 9.56E-11 | 3.60 | 9.63E-12 | 3.99 | 2.02E-11 | 3.99 | 4.07E-09 | 2.64 | |
| 512 | 3.04E-10 | 3.99 | 5.98E-13 | 3.98 | 1.06E-12 | 3.90 | 1.06E-12 | 3.90 | 7.59E-12 | 3.65 | 6.04E-13 | 4.00 | 1.27E-12 | 3.99 | 6.49E-10 | 2.65 | |
| 1 024 | 2.91E-11 | 3.99 | 3.78E-14 | 3.98 | 7.02E-14 | 3.91 | 7.02E-14 | 3.91 | 5.87E-13 | 3.69 | 3.81E-14 | 3.99 | 7.96E-14 | 4.00 | 1.03E-10 | 2.66 | |
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