Name
Title | ||
|---|---|---|
Adaptive finite element methods for an optimal control problem involving Dirac measures |
Abstract | ||
|---|---|---|
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the minimization of a cost functional that involves point evaluations of the state, thus leading to an adjoint problem with Dirac measures on the right hand side; control constraints are also considered. The proposed error estimator relies on a posteriori error estimates in the maximum norm for the state and in Muckenhoupt weighted Sobolev spaces for the adjoint state. We present an analysis that is valid for two and three-dimensional domains. We conclude by presenting several numerical experiments which reveal the competitive performance of adaptive methods based on the devised error estimator. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s00211-017-0867-9 | Numerische Mathematik |
Keywords | Field | DocType |
Pointwise tracking optimal control problem, Dirac measures, A posteriori error analysis, Adaptive finite elements, Maximum norm, Muckenhoupt weights, Weighted Sobolev spaces, 49J20, 49M25, 65K10, 65N15, 65N30, 65N50, 65Y20 | Mathematical optimization,Optimal control,Mathematical analysis,Sobolev space,A priori and a posteriori,Finite element method,Minification,Dirac (video compression format),Mathematics,Estimator,Pointwise | Journal |
Volume | Issue | ISSN |
137 | 1 | 0029-599X |
Citations | PageRank | References |
0 | 0.34 | 19 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alejandro Allendes | 1 | 4 | 3.92 |
| Enrique Otárola | 2 | 86 | 13.91 |
| Richard Rankin | 3 | 0 | 1.35 |
| Abner J. Salgado | 4 | 105 | 13.27 |