Table 3 Numerical results on adaptive meshes, Example 2
From: Adaptive variational discretization approximation method for parabolic optimal control problems
Adaptive meshes | 1 | 2 | 3 | 4 |
Nodes | 139 | 445 | 716 | 739 |
\(|\!|\!|u-u_{h}|\!|\!|\) | 9.33794e−02 | 4.53875e−02 | 4.53241e−02 | 4.53216e−02 |
\(|\!|\!|\nabla y- \nabla y_{h}|\!|\!|\) | 4.29891e+00 | 2.19612e+00 | 1.45671e+00 | 1.42490e+00 |
\(|\!|\!|\nabla p- \nabla p_{h}|\!|\!|\) | 4.30707e+00 | 2.21794e+00 | 1.49066e+00 | 1.45962e+00 |
\(|\!|\!|G_{h} y_{h}- \nabla y_{h}|\!|\!|\) | 4.78789e+00 | 2.29456e+00 | 1.46836e+00 | 1.43600e+00 |
\(|\!|\!|G_{h} p_{h}- \nabla p_{h}|\!|\!|\) | 4.71907e+00 | 2.26074e+00 | 1.44664e+00 | 1.41476e+00 |