Table 1 Numerical results, Example 1
From: Adaptive variational discretization approximation method for parabolic optimal control problems
h | k | \(|\!|\!|u-u_{h}|\!|\!|\) | Rate | \(|\!|\!|P_{h}y-y_{h}|\!|\!|_{1}\) | Rate | \(|\!|\!|P_{h}p-p_{h}|\!|\!|_{1}\) | Rate |
|---|---|---|---|---|---|---|---|
\(\frac{1}{10}\) | \(\frac{1}{10}\) | 4.59597e−02 | – | 7.21635e−03 | – | 9.51033e−03 | – |
\(\frac{1}{20}\) | \(\frac{1}{40}\) | 1.23011e−02 | 1.90 | 1.70370e−03 | 2.08 | 2.24615e−03 | 2.08 |
\(\frac{1}{40}\) | \(\frac{1}{160}\) | 3.11887e−03 | 1.97 | 4.22468e−04 | 2.01 | 5.55263e−04 | 2.01 |
\(\frac{1}{80}\) | \(\frac{1}{640}\) | 7.81133e−04 | 1.99 | 1.05482e−04 | 2.00 | 1.38467e−04 | 2.00 |