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Theory and Modern Applications

Table 3 The errors of two-grid variational multiscale method ( 4.1 ) for the steady natural convection equations

From: A variational multiscale method for steady natural convection problem based on two-grid discretization

1/ H

1/ h

\(\boldsymbol {\frac{\|\nabla(u-u_{h})\|_{0}}{\|\nabla u\|_{0}}}\)

Rate

\(\boldsymbol {\frac{\|p-p_{h}\|_{0}}{\|p\|_{0}}}\)

Rate

\(\boldsymbol {\frac{\|\nabla(T-T_{h})\|_{0}}{\|\nabla T\|_{0}}}\)

Rate

CPU(S)

2

4

0.166184

-

0.0485766

-

0.0962505

-

0.044

3

9

0.0354715

1.90444

0.00956675

2.00369

0.0211715

1.86736

0.143

4

16

0.0114202

1.96978

0.00302598

2.00057

0.00682667

1.96713

0.393

5

25

0.00470301

1.98792

0.00123938

2.00012

0.00281136

1.98788

0.915

6

36

0.00227273

1.99434

0.000597686

2.00003

0.0013585

1.99451

1.834

7

49

0.00122789

1.99702

0.000322615

2.00001

0.000733929

1.99716

3.390