| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 22 | |
| Number of page(s) | 33 | |
| DOI | https://doi.org/10.1051/cocv/2022016 | |
| Published online | 17 March 2022 | |
Optimal Borel measure controls for the two-dimensional stationary Boussinesq system
Department of Mathematics and Computer Science, University of the Philippines Baguio,
Governor Pack Road,
2600
Baguio, Philippines
* Corresponding author: grperalta@up.edu.ph
Received:
19
June
2020
Accepted:
15
February
2022
We analyze an optimal control problem for the stationary two-dimensional Boussinesq system with controls taken in the space of regular Borel measures. Such measure-valued controls are known to produce sparse solutions. First-order and second-order necessary and sufficient optimality conditions are established. Following an optimize-then-discretize strategy, the corresponding finite element approximation will be solved by a semi-smooth Newton method initialized by a continuation strategy. The controls are discretized by finite linear combinations of Dirac measures concentrated at the nodes associated with the degrees of freedom for the mini-finite element.
Mathematics Subject Classification: 49J20 / 49K20 / 49M15
Key words: Boussinesq system / Borel measures / sparse controls / optimality conditions / finite elements / semi-smooth Newton algorithm
© The authors. Published by EDP Sciences, SMAI 2022
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