Open Access
Table 4
-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 | 3.98E-03 | 4.83 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | 3.98E-03 | 2.00 | |
| 16 | 9.93E-04 | 3.42 | 9.93E-04 | 2.00 | 9.93E-04 | 2.00 | 9.93E-04 | 2.00 | 9.93E-04 | 2.00 | 9.93E-04 | 2.00 | 9.93E-04 | 2.00 | 9.93E-04 | 2.00 | |
| 32 | 2.48E-04 | 2.95 | 2.48E-04 | 2.00 | 2.48E-04 | 2.00 | 2.48E-04 | 2.00 | 2.48E-04 | 2.00 | 2.48E-04 | 2.00 | 2.48E-04 | 2.00 | 2.48E-04 | 2.00 | |
| 64 | 6.21E-05 | 2.71 | 6.21E-05 | 2.00 | 6.21E-05 | 2.00 | 6.21E-05 | 2.00 | 6.21E-05 | 2.00 | 6.21E-05 | 2.00 | 6.21E-05 | 2.00 | 6.21E-05 | 2.00 | |
| 128 | 1.55E-05 | 2.57 | 1.55E-05 | 2.00 | 1.55E-05 | 2.00 | 1.55E-05 | 2.00 | 1.55E-05 | 2.00 | 1.55E-05 | 2.00 | 1.55E-05 | 2.00 | 1.55E-05 | 2.00 | |
| 256 | 3.88E-06 | 2.48 | 3.88E-06 | 2.00 | 3.88E-06 | 2.00 | 3.88E-06 | 2.00 | 3.88E-06 | 2.00 | 3.88E-06 | 2.00 | 3.88E-06 | 2.00 | 3.88E-06 | 2.00 | |
| 512 | 9.70E-07 | 2.41 | 9.70E-07 | 2.00 | 9.70E-07 | 2.00 | 9.70E-07 | 2.00 | 9.70E-07 | 2.00 | 9.70E-07 | 2.00 | 9.70E-07 | 2.00 | 9.70E-07 | 2.00 | |
| 1 024 | 2.43E-07 | 2.36 | 2.42E-07 | 2.00 | 2.42E-07 | 2.00 | 2.42E-07 | 2.00 | 2.42E-07 | 2.00 | 2.42E-07 | 2.00 | 2.42E-07 | 2.00 | 2.42E-07 | 2.00 | |
| 2 | 4 | 4.03E-04 | ― | 4.03E-04 | ― | 4.03E-04 | ― | 4.03E-04 | ― | 4.03E-04 | ― | 4.03E-04 | ― | 4.03E-04 | ― | 4.03E-04 | ― |
| 8 | 5.12E-05 | 7.17 | 5.11E-05 | 2.98 | 5.11E-05 | 2.98 | 5.11E-05 | 2.98 | 5.11E-05 | 2.98 | 5.11E-05 | 2.98 | 5.11E-05 | 2.98 | 5.12E-05 | 2.98 | |
| 16 | 6.44E-06 | 5.11 | 6.42E-06 | 2.99 | 6.42E-06 | 2.99 | 6.42E-06 | 2.99 | 6.42E-06 | 2.99 | 6.42E-06 | 2.99 | 6.42E-06 | 2.99 | 6.42E-06 | 2.99 | |
| 32 | 8.14E-07 | 4.40 | 8.03E-07 | 3.00 | 8.03E-07 | 3.00 | 8.03E-07 | 3.00 | 8.03E-07 | 3.00 | 8.03E-07 | 3.00 | 8.03E-07 | 3.00 | 8.08E-07 | 2.99 | |
| 64 | 1.05E-07 | 4.01 | 1.00E-07 | 3.00 | 1.00E-07 | 3.00 | 1.00E-07 | 3.00 | 1.00E-07 | 3.00 | 1.00E-07 | 3.00 | 1.00E-07 | 3.00 | 1.03E-07 | 2.97 | |
| 128 | 1.40E-08 | 3.73 | 1.25E-08 | 3.00 | 1.25E-08 | 3.00 | 1.25E-08 | 3.00 | 1.26E-08 | 3.00 | 1.25E-08 | 3.00 | 1.25E-08 | 3.00 | 1.40E-08 | 2.88 | |
| 256 | 1.96E-09 | 3.51 | 1.57E-09 | 3.00 | 1.57E-09 | 3.00 | 1.57E-09 | 3.00 | 1.57E-09 | 3.00 | 1.57E-09 | 3.00 | 1.57E-09 | 3.00 | 2.22E-09 | 2.66 | |
| 512 | 2.89E-10 | 3.33 | 1.96E-10 | 3.00 | 1.96E-10 | 3.00 | 1.96E-10 | 3.00 | 1.97E-10 | 3.00 | 1.96E-10 | 3.00 | 1.96E-10 | 3.00 | 4.41E-10 | 2.33 | |
| 1 024 | 4.41E-11 | 3.20 | 2.45E-11 | 3.00 | 2.45E-11 | 3.00 | 2.45E-11 | 3.00 | 2.46E-11 | 3.00 | 2.45E-11 | 3.00 | 2.45E-11 | 3.00 | 1.02E-10 | 2.11 | |
| 3 | 4 | 2.13E-05 | ― | 2.12E-05 | ― | 2.12E-05 | ― | 2.12E-05 | ― | 2.12E-05 | ― | 2.12E-05 | ― | 2.12E-05 | ― | 2.12E-05 | ― |
| 8 | 1.38E-06 | 9.50 | 1.32E-06 | 4.00 | 1.32E-06 | 4.00 | 1.32E-06 | 4.00 | 1.33E-06 | 4.00 | 1.32E-06 | 4.00 | 1.32E-06 | 4.00 | 1.35E-06 | 3.98 | |
| 16 | 1.27E-07 | 5.88 | 8.28E-08 | 4.00 | 8.28E-08 | 4.00 | 8.28E-08 | 4.00 | 8.38E-08 | 3.99 | 8.28E-08 | 4.00 | 8.28E-08 | 4.00 | 9.79E-08 | 3.78 | |
| 32 | 1.76E-08 | 4.21 | 5.17E-09 | 4.00 | 5.18E-09 | 4.00 | 5.18E-09 | 4.00 | 5.36E-09 | 3.97 | 5.17E-09 | 4.00 | 5.18E-09 | 4.00 | 1.06E-08 | 3.21 | |
| 64 | 2.35E-09 | 3.94 | 3.24E-10 | 4.00 | 3.24E-10 | 4.00 | 3.24E-10 | 4.00 | 3.50E-10 | 3.94 | 3.24E-10 | 4.00 | 3.24E-10 | 4.00 | 1.59E-09 | 2.73 | |
| 128 | 2.79E-10 | 3.95 | 2.02E-11 | 4.00 | 2.03E-11 | 4.00 | 2.03E-11 | 4.00 | 2.33E-11 | 3.91 | 2.02E-11 | 4.00 | 2.03E-11 | 4.00 | 2.54E-10 | 2.64 | |
| 256 | 3.01E-11 | 3.98 | 1.31E-12 | 3.95 | 1.32E-12 | 3.95 | 1.32E-12 | 3.95 | 1.61E-12 | 3.85 | 1.31E-12 | 3.95 | 1.32E-12 | 3.95 | 4.08E-11 | 2.64 | |
| 512 | 3.18E-12 | 3.91 | 3.62E-13 | ― | 3.34E-13 | ― | 3.34E-13 | ― | 3.44E-13 | ― | 3.62E-13 | ― | 3.34E-13 | ― | 6.49E-12 | 2.65 | |
| 1 024 | 3.63E-13 | ― | 3.57E-13 | ― | 3.37E-13 | ― | 3.37E-13 | ― | 3.38E-13 | ― | 3.57E-13 | ― | 3.37E-13 | ― | 1.08E-12 | 2.59 | |
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