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Journal of Inequalities and Applications

Table 3 The smallest eigenvalue solved by Algorithm 3 and Algorithm 3M

From: Adaptive Morley element algorithms for the biharmonic eigenvalue problem

l

\(N_{\mathrm{dof}}\)

\(h_{l}\)

\(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\)

\(\lambda_{1,h_{l}}^{F}\)

CPU(s)

\(N_{\mathrm{dof}}\)

\(h_{l}\)

\(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\)

\(\lambda_{1,h_{l}}^{FM}\)

CPU(s)

1

2945

0.044

0.210

6333.637

0.086

2945

0.044

0.210

6333.637

0.086

2

2957

0.044

0.297

6373.503

0.137

2957

0.044

0.297

6373.503

0.137

3

3031

0.044

0.354

6538.971

0.187

3031

0.044

0.354

6538.971

0.187

4

3067

0.044

0.420

6443.737

0.244

3067

0.044

0.420

6443.737

0.245

5

3237

0.044

0.500

6489.761

0.299

3237

0.044

0.500

6489.761

0.300

6

3445

0.044

0.595

6523.466

0.358

3445

0.044

0.595

6523.466

0.360

7

3811

0.044

0.707

6566.620

0.423

3811

0.044

0.707

6566.620

0.426

8

4195

0.044

0.841

6595.431

0.496

4195

0.044

0.841

6595.431

0.498

9

4678

0.044

1.00

6597.955

0.577

4678

0.044

1.00

6597.955

0.581

10

5293

0.044

1.19

6607.441

0.670

5293

0.044

1.19

6607.441

0.696

11

6118

0.044

1.41

6623.248

0.779

25,297

0.022

0.841

6683.573

1.14

12

6997

0.044

1.68

6634.588

0.903

27,723

0.022

1.00

6686.324

1.62

13

8232

0.044

2.00

6648.804

1.05

30,933

0.022

1.19

6688.518

2.37

14

9527

0.044

2.38

6658.106

1.21

139,409

0.011

0.841

6700.069

5.85

15

11,102

0.044

2.83

6663.393

1.41

153,179

0.011

1.00

6701.996

9.71

16

12,928

0.044

3.36

6667.166

1.64

164,253

0.011

1.19

6701.274

15.2

17

15,139

0.044

4.00

6673.763

1.93

715,319

0.006

0.841

6702.994

38.2

18

17,619

0.044

4.76

6678.433

2.25

780,735

0.006

1.00

6703.096

63.8

19

20,763

0.044

5.66

6682.562

2.63

853,934

0.006

1.19

6703.205

100

20

24,365

0.044

6.73

6685.164

3.08

3,774,935

0.003

0.841

6703.503

231

21

28,967

0.044

8.00

6687.944

3.60

4,083,915

0.003

1.00

6703.538

372

22

34,068

0.044

9.51

6690.675

4.21

–

–

–

–

–

23

40,007

0.044

11.3

6692.914

4.97

–

–

–

–

–

24

47,117

0.044

13.5

6694.937

5.89

–

–

–

–

–

25

55,275

0.044

16.0

6696.294

6.98

–

–

–

–

–

26

64,407

0.044

19.0

6696.867

8.28

–

–

–

–

–

27

75,259

0.031

13.5

6697.823

9.85

–

–

–

–

–

28

88,357

0.031

16.0

6698.753

12.0

–

–

–

–

–

29

104,277

0.031

19.0

6699.461

14.6

–

–

–

–

–

30

123,275

0.031

22.6

6700.132

17.7

–

–

–

–

–

31

145,073

0.031

26.9

6700.784

21.4

–

–

–

–

–

32

170,409

0.022

22.6

6701.303

25.9

–

–

–

–

–

33

199,844

0.022

26.9

6701.644

31.2

–

–

–

–

–

34

235,273

0.022

26.9

6701.901

37.6

–

–

–

–

–

35

272,825

0.022

32.0

6702.117

45.7

–

–

–

–

–

36

319,389

0.022

38.1

6702.299

55.5

–

–

–

–

–

37

375,188

0.022

45.3

6702.459

67.4

–

–

–

–

–

38

443,902

0.022

53.8

6702.642

81.7

–

–

–

–

–

39

522,189

0.022

64.0

6702.815

98.8

–

–

–

–

–

40

612,931

0.022

76.1

6702.966

119

–

–

–

–

–

41

718,761

0.016

53.8

6703.061

143

–

–

–

–

–

42

844,127

0.016

64.0

6703.150

171

–

–

–

–

–

43

988,405

0.016

76.1

6703.208

205

–

–

–

–

–

44

1,149,526

0.016

90.5

6703.256

244

–

–

–

–

–

45

1,346,037

0.016

108

6703.295

291

–

–

–

–

–

46

1,583,069

0.016

128

6703.340

347

–

–

–

–

–

47

1,872,353

0.016

152

6703.381

412

–

–

–

–

–

48

2,194,659

0.011

108

6703.425

490

–

–

–

–

–

49

2,570,539

0.011

128

6703.458

580

–

–

–

–

–

50

3,008,669

0.011

152

6703.478

687

–

–

–

–

–

51

3,535,715

0.011

181

6703.498

813

–

–

–

–

–

52

4,118,331

0.011

215

6703.512

962

–

–

–

–

–

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