A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state
We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly f...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
18 February 2011
|
| In: |
Numerische Mathematik
Year: 2011, Volume: 118, Issue: 3, Pages: 587-600 |
| ISSN: | 0945-3245 |
| DOI: | 10.1007/s00211-011-0360-9 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s00211-011-0360-9
|
| Author Notes: | C. Ortner, W. Wollner |
| Summary: | We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W1,∞-error of the finite element projection, without using adjoint information. If the control space is discretized directly, we first prove a regularity result for the optimal control to control the approximation error, based on which we then obtain analogous convergence rates. |
|---|---|
| Item Description: | Gesehen am 13.10.2022 |
| Physical Description: | Online Resource |
| ISSN: | 0945-3245 |
| DOI: | 10.1007/s00211-011-0360-9 |