k

Analytical

${\lambda }_k$ [32]

Computed Eigenvalue ${\lambda }_k^{\left(Gal.\right)}$

Bernstein Polynomial

Finite Element

${\lambda }_k^{\left(Gal.\right)}$ 8 × 8 [32]

Rel. Error

Bernstein Polynomial

Rel. Error

8 × 8 [32]

n = 8

n = 10

Triangular

Linear

Rectangular

Linear

n = 8

n = 10

Triangular

Linear

Rectangular

Linear

1

3.9270

3.926991

3.926991

4.0025

3.9522

2.292e-06

2.339e-06

1.921e-02

6.417e-03

2

4.9673

4.967296

4.967294

5.2068

5.0478

8.053e-07

1.181e-06

4.822e-02

1.621e-02

3

6.3321

6.332157

6.332083

6.8788

6.6020

9.002e-06

2.737e-06

8.634e-02

4.262e-02

4

7.2410

7.241018

7.241013

7.5271

7.4200

2.486e-06

1.834e-06

3.951e-02

2.472e-02

5

7.8540

7.853987

7.853982

8.4565

8.0571

1.655e-06

2.338e-06

7.671e-02

2.587e-02

6

7.8540

7.895219

7.853989

8.8856

8.5145

5.248e-03

1.457e-06

1.313e-01

8.410e-02

7

8.7810

8.781076

8.781019

9.9280

9.1117

8.655e-06

2.117e-06

1.316e-01

3.765e-02

8

9.4574

9.583454

9.462444

11.1193

10.5797

1.331e-02

5.334e-04

1.757e-01

1.187e-01

9

9.9346

9.967225

9.934594

11.4425

10.7280

3.284e-03

6.303e-07

1.518e-01

7.986e-02