Theory and Modern Applications
Table 1 The errors of standard Galerkin FEM ( 2.8 ) 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 | 0.166184 | - | 0.0485766 | - | 0.0962482 | - | 0.066 |
9 | 0.0354715 | 1.90444 | 0.00956673 | 2.00369 | 0.0211698 | 1.86743 | 0.305 |
16 | 0.0114207 | 1.96978 | 0.00302598 | 2.00057 | 0.00682614 | 1.96713 | 0.977 |
25 | 0.00470301 | 1.98792 | 0.00123938 | 2.00012 | 0.0028114 | 1.98789 | 2.503 |
36 | 0.00227273 | 1.99434 | 0.000597686 | 2.00003 | 0.00135839 | 1.99453 | 5.081 |
49 | 0.00122789 | 1.99702 | 0.000322615 | 2.00001 | 0.000733861 | 1.99718 | 9.981 |