Open Access
Table 7
-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-06 | ― | 5.90E-06 | ― | 6.04E-06 | ― | 6.04E-06 | ― | 6.79E-06 | ― | 1.19E-05 | ― | 1.34E-05 | ― | 7.32E-06 | ― |
| 8 | 5.46E-06 | 1.59 | 2.29E-06 | 1.37 | 2.35E-06 | 1.36 | 2.35E-06 | 1.36 | 3.16E-06 | 1.11 | 3.17E-06 | 1.91 | 4.42E-06 | 1.60 | 4.59E-06 | 0.67 | |
| 16 | 2.70E-06 | 1.73 | 7.16E-07 | 1.68 | 7.58E-07 | 1.63 | 7.58E-07 | 1.63 | 1.16E-06 | 1.45 | 8.39E-07 | 1.92 | 1.23E-06 | 1.85 | 2.08E-06 | 1.14 | |
| 32 | 1.14E-06 | 1.84 | 2.02E-07 | 1.82 | 2.23E-07 | 1.76 | 2.23E-07 | 1.76 | 3.83E-07 | 1.60 | 2.19E-07 | 1.94 | 3.29E-07 | 1.90 | 9.06E-07 | 1.20 | |
| 64 | 4.28E-07 | 1.91 | 5.41E-08 | 1.90 | 6.21E-08 | 1.84 | 6.21E-08 | 1.84 | 1.19E-07 | 1.69 | 5.62E-08 | 1.96 | 8.54E-08 | 1.94 | 3.80E-07 | 1.25 | |
| 128 | 1.50E-07 | 1.95 | 1.40E-08 | 1.95 | 1.67E-08 | 1.89 | 1.67E-08 | 1.89 | 3.53E-08 | 1.75 | 1.43E-08 | 1.97 | 2.18E-08 | 1.97 | 1.56E-07 | 1.29 | |
| 256 | 4.95E-08 | 1.97 | 3.58E-09 | 1.97 | 4.41E-09 | 1.92 | 4.41E-09 | 1.92 | 1.02E-08 | 1.79 | 3.62E-09 | 1.98 | 5.52E-09 | 1.98 | 6.29E-08 | 1.31 | |
| 512 | 1.58E-08 | 1.99 | 9.05E-10 | 1.98 | 1.15E-09 | 1.94 | 1.15E-09 | 1.94 | 2.88E-09 | 1.82 | 9.10E-10 | 1.99 | 1.39E-09 | 1.99 | 2.53E-08 | 1.32 | |
| 1 024 | 4.90E-09 | 1.99 | 2.28E-10 | 1.99 | 2.95E-10 | 1.96 | 2.95E-10 | 1.96 | 8.02E-10 | 1.84 | 2.28E-10 | 1.99 | 3.48E-10 | 2.00 | 1.01E-08 | 1.32 | |
| 2 | 4 | 2.91E-06 | ― | 1.51E-06 | ― | 1.63E-06 | ― | 1.63E-06 | ― | 2.09E-06 | ― | 3.98E-06 | ― | 5.33E-06 | ― | 2.39E-06 | ― |
| 8 | 1.45E-06 | 2.41 | 3.36E-07 | 2.17 | 3.61E-07 | 2.18 | 3.61E-07 | 2.18 | 5.91E-07 | 1.82 | 5.28E-07 | 2.91 | 9.52E-07 | 2.49 | 1.09E-06 | 1.13 | |
| 16 | 5.01E-07 | 2.63 | 5.57E-08 | 2.59 | 6.25E-08 | 2.53 | 6.25E-08 | 2.53 | 1.25E-07 | 2.24 | 6.95E-08 | 2.93 | 1.31E-07 | 2.86 | 3.23E-07 | 1.75 | |
| 32 | 1.35E-07 | 2.80 | 8.06E-09 | 2.79 | 9.65E-09 | 2.69 | 9.65E-09 | 2.69 | 2.31E-08 | 2.44 | 9.00E-09 | 2.95 | 1.74E-08 | 2.91 | 8.95E-08 | 1.85 | |
| 64 | 3.06E-08 | 2.90 | 1.09E-09 | 2.89 | 1.39E-09 | 2.79 | 1.39E-09 | 2.79 | 3.92E-09 | 2.56 | 1.15E-09 | 2.97 | 2.25E-09 | 2.95 | 2.38E-08 | 1.91 | |
| 128 | 6.25E-09 | 2.95 | 1.42E-10 | 2.94 | 1.92E-10 | 2.86 | 1.92E-10 | 2.86 | 6.27E-10 | 2.64 | 1.46E-10 | 2.98 | 2.87E-10 | 2.97 | 6.14E-09 | 1.95 | |
| 256 | 1.18E-09 | 2.97 | 1.82E-11 | 2.97 | 2.58E-11 | 2.89 | 2.58E-11 | 2.89 | 9.65E-11 | 2.70 | 1.84E-11 | 2.99 | 3.62E-11 | 2.99 | 1.57E-09 | 1.97 | |
| 512 | 2.12E-10 | 2.99 | 2.32E-12 | 2.97 | 3.42E-12 | 2.92 | 3.42E-12 | 2.92 | 1.45E-11 | 2.74 | 2.35E-12 | 2.97 | 4.56E-12 | 2.99 | 3.96E-10 | 1.98 | |
| 1 024 | 3.67E-11 | 2.99 | 4.55E-13 | ― | 5.53E-13 | ― | 5.53E-13 | ― | 2.15E-12 | 2.75 | 4.65E-13 | ― | 6.58E-13 | ― | 9.95E-11 | 1.99 | |
| 3 | 4 | 9.92E-07 | ― | 3.87E-07 | ― | 4.50E-07 | ― | 4.50E-07 | ― | 6.54E-07 | ― | 1.40E-06 | ― | 2.15E-06 | ― | 7.88E-07 | ― |
| 8 | 3.97E-07 | 3.18 | 4.99E-08 | 2.95 | 5.68E-08 | 2.99 | 5.68E-08 | 2.99 | 1.13E-07 | 2.53 | 9.03E-08 | 3.95 | 2.09E-07 | 3.36 | 2.66E-07 | 1.57 | |
| 16 | 9.68E-08 | 3.48 | 4.40E-09 | 3.50 | 5.33E-09 | 3.41 | 5.33E-09 | 3.41 | 1.41E-08 | 3.01 | 5.86E-09 | 3.95 | 1.44E-08 | 3.86 | 5.25E-08 | 2.34 | |
| 32 | 1.68E-08 | 3.73 | 3.28E-10 | 3.75 | 4.33E-10 | 3.62 | 4.33E-10 | 3.62 | 1.45E-09 | 3.28 | 3.77E-10 | 3.96 | 9.55E-10 | 3.92 | 9.20E-09 | 2.51 | |
| 64 | 2.33E-09 | 3.87 | 2.24E-11 | 3.87 | 3.23E-11 | 3.74 | 3.23E-11 | 3.74 | 1.35E-10 | 3.43 | 2.41E-11 | 3.97 | 6.17E-11 | 3.95 | 1.55E-09 | 2.57 | |
| 128 | 2.78E-10 | 3.94 | 1.51E-12 | 3.89 | 2.31E-12 | 3.81 | 2.31E-12 | 3.81 | 1.16E-11 | 3.53 | 1.55E-12 | 3.95 | 3.93E-12 | 3.97 | 2.53E-10 | 2.61 | |
| 256 | 3.01E-11 | 3.97 | 3.68E-13 | ― | 3.82E-13 | ― | 3.82E-13 | ― | 1.00E-12 | 3.53 | 3.54E-13 | ― | 4.05E-13 | ― | 4.07E-11 | 2.64 | |
| 512 | 3.18E-12 | 3.91 | 3.53E-13 | ― | 3.24E-13 | ― | 3.24E-13 | ― | 3.35E-13 | ― | 3.73E-13 | ― | 3.48E-13 | ― | 6.49E-12 | 2.65 | |
| 1 024 | 3.63E-13 | ― | 3.57E-13 | ― | 3.37E-13 | ― | 3.37E-13 | ― | 3.38E-13 | ― | 3.56E-13 | ― | 3.38E-13 | ― | 1.08E-12 | 2.59 | |
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