Theory and Modern Applications
Table 3 Numerical results for Example 2 with \(\pmb{\tau=2^{-10}}\)
β | h | 1/16 | 1/32 | 1/64 | 1/128 | Order |
|---|---|---|---|---|---|---|
1/4 | \(\Vert u-u_{h} \Vert \) | 3.62e−02 | 1.91e−02 | 9.77e−03 | 4.95e−03 | 0.99 |
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) | 6.51e−02 | 3.84e−02 | 2.28e−02 | 1.35e−02 | 0.75 | |
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) | 1.13e−02 | 7.26e−03 | 4.69e−03 | 3.04e−03 | 0.63 | |
1/2 | \(\Vert u-u_{h} \Vert \) | 3.62e−02 | 1.91e−02 | 9.77e−03 | 4.95e−03 | 0.99 |
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) | 1.84e−02 | 9.04e−03 | 4.48e−03 | 2.23e−03 | 1.00 | |
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) | 1.03e−02 | 6.11e−03 | 3.62e−03 | 2.15e−03 | 0.75 | |
2/3 | \(\Vert u-u_{h} \Vert \) | 3.62e−02 | 1.91e−02 | 9.77e−03 | 4.95e−03 | 0.99 |
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) | 6.86e−03 | 2.99e−03 | 1.31e−03 | 5.82e−04 | 1.15 | |
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) | 8.18e−03 | 4.59e−03 | 2.58e−03 | 1.46e−03 | 0.82 |