Gudi, T and Sau, RC (2020) Finite element analysis of the constrained Dirichlet boundary control problem governed by the diffusion problem. In: ESAIM - Control, Optimisation and Calculus of Variations, 26 .
Full text not available from this repository.Abstract
We study an energy space-based approach for the Dirichlet boundary optimal control problem governed by the Laplace equation with control constraints. The optimality system results in a simplified Signorini type problem for control which is coupled with boundary value problems for state and costate variables. We propose a finite element based numerical method using the linear Lagrange finite element spaces with discrete control constraints at the Lagrange nodes. The analysis is presented in a combination for both the gradient and the L2 cost functional. A priori error estimates of optimal order in the energy norm is derived up to the regularity of the solution for both the cases. Theoretical results are illustrated by some numerical experiments. © 2020 EDP Sciences, SMAI.
| Item Type: | Journal Article |
|---|---|
| Publication: | ESAIM - Control, Optimisation and Calculus of Variations |
| Publisher: | EDP Sciences |
| Additional Information: | The copyright of this article belongs to EDP Sciences |
| Keywords: | Boundary value problems; Lagrange multipliers; Numerical methods; Optimal control systems, Control constraint; Diffusion problems; Dirichlet boundary; Dirichlet boundary controls; Lagrange finite elements; Numerical experiments; Optimality system; Priori error estimate, Finite element method |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 15 Mar 2021 09:23 |
| Last Modified: | 15 Mar 2021 09:23 |
| URI: | http://eprints.iisc.ac.in/id/eprint/67458 |
Actions (login required)
 |
View Item |
