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Table 1 The smallest eigenvalue solved by Algorithm 1 and Algorithm 1M

From: Adaptive Morley element algorithms for the biharmonic eigenvalue problem

l \(N_{\mathrm{dof}}\) \(h_{l}\) \(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\) \(\lambda_{1,h_{l}}\) CPU(s) \(N_{\mathrm{dof}}\) \(h_{l}\) \(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\) \(\lambda_{1,h_{l}}^{M}\) CPU(s)
1 2945 0.044 0.210 6333.637 0.275 2945 0.044 0.210 6333.637 0.086
2 2957 0.044 0.250 6368.756 0.368 2957 0.044 0.250 6368.756 0.162
3 3035 0.044 0.297 6426.312 0.452 3035 0.044 0.297 6426.312 0.239
4 3135 0.044 0.354 6459.396 0.537 3135 0.044 0.354 6459.396 0.320
5 3345 0.044 0.420 6506.181 0.629 3345 0.044 0.420 6506.181 0.405
6 3609 0.044 0.500 6540.464 0.726 3609 0.044 0.500 6540.464 0.499
7 3979 0.044 0.595 6574.027 0.834 3979 0.044 0.595 6574.027 0.605
8 4459 0.044 0.707 6588.671 0.957 4459 0.044 0.707 6588.671 0.723
9 5097 0.044 0.841 6606.244 1.10 5097 0.044 0.841 6606.244 0.860
10 5787 0.044 1.00 6615.776 1.27 5787 0.044 1.00 6615.776 1.02
11 6665 0.044 1.19 6631.992 1.48 6665 0.044 1.19 6631.992 1.21
12 7791 0.044 1.41 6642.939 1.71 31,697 0.022 0.841 6688.240 2.12
13 9110 0.044 1.68 6656.854 1.97 34,833 0.022 1.00 6690.595 3.15
14 10,591 0.044 2.00 6662.468 2.27 39,191 0.022 1.19 6693.066 4.43
15 12,295 0.044 2.38 6665.980 2.65 173,919 0.011 0.841 6701.061 11.4
16 14,331 0.044 2.83 6671.824 3.10 189,989 0.011 1.00 6701.477 19.4
17 16,641 0.044 3.36 6676.967 3.62 211,977 0.011 1.19 6701.750 29.0
18 19,497 0.044 4.00 6680.844 4.21 948,969 0.006 0.841 6703.147 82.8
19 22,925 0.044 4.76 6684.502 4.92 1,025,149 0.006 1.00 6703.198 141
20 27,171 0.044 5.66 6686.546 5.77 1,131,177 0.006 1.19 6703.244 210
21 32,088 0.044 6.73 6689.797 6.76 5,114,697 0.003 0.841 6703.512 587
22 37,703 0.044 8.00 6692.349 7.95
23 44,289 0.044 9.51 6694.425 9.39
24 52,103 0.044 11.3 6695.960 11.1
25 60,857 0.044 13.5 6696.560 13.2
26 70,881 0.044 16.0 6697.400 15.7
27 83,091 0.031 13.5 6698.304 18.7
28 98,019 0.031 16.0 6699.274 22.7
29 116,273 0.031 19.0 6699.950 27.4
30 136,557 0.031 22.6 6700.589 33.1
31 160,465 0.022 16.0 6701.087 40.0
32 188,195 0.022 19.0 6701.469 48.2
33 221,401 0.022 22.6 6701.858 58.0
34 257,797 0.022 26.9 6702.060 69.7
35 301,063 0.022 32.0 6702.246 84.6
36 353,201 0.022 38.1 6702.411 102
37 416,609 0.022 45.3 6702.557 124
38 492,039 0.022 45.3 6702.767 151
39 577,233 0.022 53.8 6702.937 182
40 677,271 0.016 45.3 6703.035 220
41 793,765 0.016 53.8 6703.115 266
42 934,557 0.016 64.0 6703.190 321
43 1,084,193 0.016 64.0 6703.237 388
44 1,267,059 0.016 76.1 6703.272 465
45 1,487,051 0.016 90.5 6703.320 558
46 1,756,709 0.016 108 6703.362 672
47 2,065,245 0.011 90.5 6703.407 809
48 2,420,223 0.011 108 6703.446 973
49 2,834,373 0.011 128 6703.468 1171
50 3,319,763 0.011 128 6703.487 1415
51 3,894,763 0.011 152 6703.505 1706
52 4,522,239 0.011 181 6703.516 2060