Theory and Modern Applications
Table 2 The errors of variational multiscale method ( 3.7 ) for the steady natural convection equations
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) |
|---|---|---|---|---|---|---|---|
4 | 0.166197 | - | 0.0485818 | - | 0.0962482 | - | 0.08 |
9 | 0.0354721 | 1.90451 | 0.009566804 | 2.0038 | 0.0211698 | 1.86743 | 0.283 |
16 | 0.0114203 | 1.96981 | 0.00302599 | 2.00059 | 0.00682614 | 1.96713 | 0.901 |
25 | 0.00470303 | 1.98793 | 0.00123938 | 2.00012 | 0.0028114 | 1.98789 | 2.207 |
36 | 0.00227273 | 1.99434 | 0.000597686 | 2.00003 | 0.00135839 | 1.99453 | 4.682 |
49 | 0.00122789 | 1.99703 | 0.000322615 | 2.00001 | 0.000733861 | 1.99718 | 8.804 |