TABLE 1B.
Computed
with 48 points on the boundary, at the same selected points
as in Table 1 A, computed
to be compared with the exact values,
are the rate of convergence when compared to the coarser grid
| Node | w1 | w2 | e1 | e2 | r1 | r2 | q1 | q2 |
|---|---|---|---|---|---|---|---|---|
| 1 | 2.000149 | −0.000091 | 1.49(−4) | 0.91(−4) | 5.63 | 0.53 | 8.40 | 0.5 |
| 2 | 1.931862 | −0.518158 | 1.04(−5) | 5.20(−4) | 9.25 | 0.94 | ||
| 3 | 1.731796 | −1.001094 | 2.55(−4) | 1.09(−3) | 3.84 | 1.07 | 1.76 | 5.03 |
| 4 | 1.413760 | −1.416040 | 4.54(−4) | 1.83(−3) | 0.65 | 0.62 | ||
| 5 | 0.999445 | −1.734516 | 5.55(−4) | 2.47(−3) | 0.96 | 0.85 | 4.33 | 1.49 |
| 6 | 0.517242 | −1.934964 | 3.96(−4) | 3.11(−3) | 1.55 | 1.20 |
are the rate of convergence when a grid of 24 points is compared to a grid with 12 points. For example, the computed error
in the fourth column means that
The rates of convergence are
when compared to the coarser grid. The computed rate of the convergence is defined by
where
are the errors in the traction for two different grids with meshes
Here
are the meshes that correspond to 24 and 48 points, respectively.
are the rate of convergence when a grid of 24 points is compared to a grid with 12 points.