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Table 2 The smallest eigenvalue solved by Algorithm 2 and Algorithm 2M

From: Adaptive Morley element algorithms for the biharmonic eigenvalue problem

l \(N_{\mathrm{dof}}\) \(h_{l}\) \(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\) \(\lambda_{1,h_{l}}^{R}\) CPU(s) \(N_{\mathrm{dof}}\) \(h_{l}\) \(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\) \(\lambda_{1,h_{l}}^{\mathrm{RM}}\) CPU(s)
1 2945 0.044 0.210 6333.637 0.133 2945 0.044 0.210 6333.637 0.090
2 2957 0.044 0.297 6373.503 0.228 2957 0.044 0.297 6373.503 0.140
3 3031 0.044 0.354 6538.971 0.280 3031 0.044 0.354 6538.971 0.192
4 3067 0.044 0.420 6443.737 0.371 3067 0.044 0.420 6443.737 0.250
5 3237 0.044 0.500 6489.761 0.426 3237 0.044 0.500 6489.761 0.305
6 3445 0.044 0.595 6523.466 0.487 3445 0.044 0.595 6523.466 0.365
7 3811 0.044 0.707 6566.620 0.560 3811 0.044 0.707 6566.620 0.431
8 4195 0.044 0.841 6595.431 0.636 4195 0.044 0.841 6595.431 0.504
9 4678 0.044 1.00 6597.955 0.720 4678 0.044 1.00 6597.955 0.588
10 5293 0.044 1.19 6607.441 0.814 5293 0.044 1.19 6607.441 0.709
11 6118 0.044 1.41 6623.248 0.924 25,297 0.022 0.841 6683.573 1.15
12 6997 0.044 1.68 6634.588 1.05 27,723 0.022 1.00 6686.324 1.63
13 8232 0.044 2.00 6648.804 1.20 30,933 0.022 1.19 6688.518 2.38
14 9527 0.044 2.38 6658.106 1.39 139,409 0.011 0.841 6700.069 5.87
15 11,102 0.044 2.83 6663.393 1.59 153,179 0.011 1.00 6700.762 9.71
16 12,928 0.044 3.36 6667.166 1.82 168,897 0.011 1.19 6701.161 15.4
17 15,139 0.044 4.00 6673.763 2.11 740,417 0.006 0.841 6702.983 39.1
18 17,619 0.044 4.76 6678.433 2.43 807,451 0.006 1.00 6703.097 65.4
19 20,763 0.044 5.66 6682.562 2.82 882,597 0.006 1.19 6703.149 103
20 24,365 0.044 6.73 6685.164 3.27 3,907,351 0.003 0.841 6703.486 236
21 28,967 0.044 8.00 6687.944 3.81 4,218,771 0.003 1.00 6703.504 382
22 34,068 0.044 9.51 6690.675 4.50
23 40,007 0.044 11.3 6692.914 5.39
24 47,117 0.044 13.5 6694.937 6.46
25 55,275 0.044 16.0 6696.294 7.64
26 64,407 0.044 19.0 6696.867 9.09
27 75,259 0.031 13.5 6697.823 10.8
28 88,353 0.031 16.0 6698.752 13.2
29 104,269 0.031 19.0 6699.457 16.1
30 123,285 0.031 22.6 6700.133 19.4
31 145,061 0.031 26.9 6700.774 23.3
32 170,397 0.022 22.6 6701.291 27.9
33 199,833 0.022 26.9 6701.638 33.5
34 235,261 0.022 26.9 6701.906 40.0
35 272,877 0.022 32.0 6702.117 48.6
36 319,549 0.022 38.1 6702.292 58.8
37 375,279 0.022 45.3 6702.462 71.1
38 444,149 0.022 53.8 6702.631 86.1
39 522,525 0.022 64.0 6702.819 104
40 613,375 0.022 76.1 6702.964 125
41 719,217 0.016 53.8 6703.062 149
42 844,333 0.016 64.0 6703.144 179
43 988,863 0.016 76.1 6703.208 214
44 1,150,057 0.016 90.5 6703.256 255
45 1,346,861 0.016 108 6703.292 304
46 1,584,041 0.016 128 6703.337 362
47 1,873,597 0.016 152 6703.378 433
48 2,196,067 0.011 108 6703.422 509
49 2,572,281 0.011 128 6703.454 598
50 3,010,543 0.011 152 6703.474 705
51 3,538,161 0.011 181 6703.497 831
52 4,120,833 0.011 215 6703.510 979