Open Access
Table 3
-error on 8 layer-adapted meshes for Example 1, 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 | 1.59E-02 | ― | 1.59E-02 | ― | 1.59E-02 | ― | 1.59E-02 | ― | 1.59E-02 | ― | 1.59E-02 | ― | 1.59E-02 | ― | 1.59E-02 | ― |
| 8 | 4.01E-03 | 4.80 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | 3.96E-03 | 2.00 | 3.97E-03 | 2.00 | 4.00E-03 | 2.00 | |
| 16 | 1.03E-03 | 3.36 | 9.94E-04 | 2.00 | 9.94E-04 | 2.00 | 9.94E-04 | 2.00 | 9.98E-04 | 2.00 | 9.91E-04 | 2.00 | 9.94E-04 | 2.00 | 1.01E-03 | 1.98 | |
| 32 | 2.73E-04 | 2.82 | 2.49E-04 | 2.00 | 2.49E-04 | 2.00 | 2.49E-04 | 2.00 | 2.51E-04 | 1.99 | 2.48E-04 | 2.00 | 2.49E-04 | 2.00 | 2.64E-04 | 1.94 | |
| 64 | 7.53E-05 | 2.52 | 6.22E-05 | 2.00 | 6.22E-05 | 2.00 | 6.22E-05 | 2.00 | 6.31E-05 | 1.99 | 6.20E-05 | 2.00 | 6.22E-05 | 2.00 | 7.26E-05 | 1.86 | |
| 128 | 2.15E-05 | 2.32 | 1.55E-05 | 2.00 | 1.56E-05 | 2.00 | 1.56E-05 | 2.00 | 1.59E-05 | 1.99 | 1.55E-05 | 2.00 | 1.56E-05 | 2.00 | 2.20E-05 | 1.73 | |
| 256 | 6.29E-06 | 2.20 | 3.90E-06 | 2.00 | 3.91E-06 | 2.00 | 3.91E-06 | 2.00 | 4.01E-06 | 1.98 | 3.89E-06 | 2.00 | 3.90E-06 | 2.00 | 7.39E-06 | 1.57 | |
| 512 | 1.86E-06 | 2.12 | 9.84E-07 | 1.99 | 9.87E-07 | 1.99 | 9.87E-07 | 1.99 | 1.02E-06 | 1.97 | 9.82E-07 | 1.99 | 9.86E-07 | 1.99 | 2.71E-06 | 1.45 | |
| 1 024 | 5.51E-07 | 2.07 | 2.53E-07 | 1.96 | 2.54E-07 | 1.96 | 2.54E-07 | 1.96 | 2.65E-07 | 1.95 | 2.53E-07 | 1.96 | 2.54E-07 | 1.96 | 1.04E-06 | 1.38 | |
| 2 | 4 | 4.97E-04 | ― | 4.30E-04 | ― | 4.34E-04 | ― | 4.34E-04 | ― | 4.53E-04 | ― | 6.32E-04 | ― | 6.35E-04 | ― | 4.68E-04 | ― |
| 8 | 1.54E-04 | 4.07 | 6.11E-05 | 2.81 | 6.25E-05 | 2.80 | 6.25E-05 | 2.80 | 7.81E-05 | 2.54 | 7.73E-05 | 3.03 | 9.72E-05 | 2.71 | 1.20E-04 | 1.96 | |
| 16 | 5.05E-05 | 2.75 | 8.48E-06 | 2.85 | 8.94E-06 | 2.80 | 8.94E-06 | 2.80 | 1.41E-05 | 2.47 | 9.64E-06 | 3.00 | 1.30E-05 | 2.91 | 3.30E-05 | 1.87 | |
| 32 | 1.35E-05 | 2.81 | 1.14E-06 | 2.90 | 1.25E-06 | 2.83 | 1.25E-06 | 2.83 | 2.45E-06 | 2.52 | 1.21E-06 | 2.99 | 1.70E-06 | 2.93 | 8.99E-06 | 1.88 | |
| 64 | 3.07E-06 | 2.90 | 1.48E-07 | 2.94 | 1.71E-07 | 2.87 | 1.71E-07 | 2.87 | 4.04E-07 | 2.60 | 1.53E-07 | 2.99 | 2.18E-07 | 2.96 | 2.38E-06 | 1.92 | |
| 128 | 6.25E-07 | 2.95 | 1.89E-08 | 2.97 | 2.29E-08 | 2.90 | 2.29E-08 | 2.90 | 6.39E-08 | 2.66 | 1.92E-08 | 2.99 | 2.77E-08 | 2.98 | 6.14E-07 | 1.95 | |
| 256 | 1.18E-07 | 2.97 | 2.40E-09 | 2.98 | 3.02E-09 | 2.92 | 3.02E-09 | 2.92 | 9.78E-09 | 2.71 | 2.42E-09 | 2.99 | 3.49E-09 | 2.99 | 1.57E-07 | 1.97 | |
| 512 | 2.12E-08 | 2.99 | 3.04E-10 | 2.98 | 3.95E-10 | 2.94 | 3.95E-10 | 2.94 | 1.46E-09 | 2.74 | 3.05E-10 | 2.99 | 4.39E-10 | 2.99 | 3.96E-08 | 1.98 | |
| 1 024 | 3.65E-09 | 2.99 | 3.87E-11 | 2.97 | 5.15E-11 | 2.94 | 5.15E-11 | 2.94 | 2.14E-10 | 2.77 | 3.88E-11 | 2.97 | 5.54E-11 | 2.99 | 9.95E-09 | 1.99 | |
| 3 | 4 | 1.01E-04 | ― | 4.41E-05 | ― | 4.97E-05 | ― | 4.97E-05 | ― | 6.87E-05 | ― | 1.71E-04 | ― | 1.82E-04 | ― | 8.16E-05 | ― |
| 8 | 3.97E-05 | 3.26 | 5.16E-06 | 3.10 | 5.83E-06 | 3.09 | 5.83E-06 | 3.09 | 1.14E-05 | 2.59 | 1.02E-05 | 4.08 | 1.76E-05 | 3.38 | 2.66E-05 | 1.62 | |
| 16 | 9.68E-06 | 3.48 | 4.48E-07 | 3.53 | 5.39E-07 | 3.44 | 5.39E-07 | 3.44 | 1.41E-06 | 3.01 | 6.25E-07 | 4.02 | 1.19E-06 | 3.89 | 5.25E-06 | 2.34 | |
| 32 | 1.68E-06 | 3.73 | 3.32E-08 | 3.75 | 4.36E-08 | 3.63 | 4.36E-08 | 3.63 | 1.45E-07 | 3.28 | 3.91E-08 | 4.00 | 7.85E-08 | 3.92 | 9.20E-07 | 2.51 | |
| 64 | 2.33E-07 | 3.87 | 2.27E-09 | 3.87 | 3.25E-09 | 3.75 | 3.25E-09 | 3.75 | 1.35E-08 | 3.43 | 2.46E-09 | 3.99 | 5.06E-09 | 3.96 | 1.55E-07 | 2.57 | |
| 128 | 2.78E-08 | 3.94 | 1.49E-10 | 3.93 | 2.30E-10 | 3.82 | 2.30E-10 | 3.82 | 1.16E-09 | 3.53 | 1.55E-10 | 3.99 | 3.22E-10 | 3.98 | 2.53E-08 | 2.61 | |
| 256 | 3.01E-09 | 3.97 | 9.53E-12 | 3.96 | 1.58E-11 | 3.87 | 1.58E-11 | 3.87 | 9.56E-11 | 3.60 | 9.71E-12 | 3.99 | 2.03E-11 | 3.99 | 4.07E-09 | 2.64 | |
| 512 | 3.04E-10 | 3.99 | 6.04E-13 | 3.98 | 1.06E-12 | 3.90 | 1.06E-12 | 3.90 | 7.59E-12 | 3.65 | 6.09E-13 | 3.99 | 1.27E-12 | 3.99 | 6.49E-10 | 2.65 | |
| 1 024 | 2.91E-11 | 3.99 | 3.82E-14 | 3.98 | 7.04E-14 | 3.91 | 7.04E-14 | 3.91 | 5.87E-13 | 3.69 | 3.84E-14 | 3.99 | 7.98E-14 | 3.99 | 1.03E-10 | 2.66 | |
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