Table 2 Numerical results on uniform meshes, Example 2
From: Adaptive variational discretization approximation method for parabolic optimal control problems
Uniform meshes | 1 | 2 | 3 | 4 |
Nodes | 121 | 441 | 1681 | 6561 |
\(|\!|\!|u-u_{h}|\!|\!|\) | 1.51170e−01 | 5.67167e−02 | 5.65961e−02 | 5.65652e−02 |
\(|\!|\!|\nabla y- \nabla y_{h}|\!|\!|\) | 5.22324e+00 | 2.69670e+00 | 1.35903e+00 | 6.80921e−01 |
\(|\!|\!|\nabla p- \nabla p_{h}|\!|\!|\) | 5.22335e+00 | 2.69667e+00 | 1.35902e+00 | 6.80944e−01 |
\(|\!|\!|G_{h} y_{h}- \nabla y_{h}|\!|\!|\) | 5.50904e+00 | 2.78499e+00 | 1.37386e+00 | 6.82949e−01 |
\(|\!|\!|G_{h} p_{h}- \nabla p_{h}|\!|\!|\) | 5.51247e+00 | 2.78475e+00 | 1.37345e+00 | 6.82704e−01 |