Error estimates for the finite element approximation of bilinear boundary control problems
Abstract
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin coefficient from a given measurement of the state, or when the Robin coefficient can be controlled in order to reach a desired state. To this end, necessary and sufficient optimality conditions are derived and several discretization approaches for the numerical solution the optimal control problem are investigated. Considered are both a full discretization and the postprocessing approach meaning that we compute an improved control by a pointwise evaluation of the first-order optimality condition. For both approaches finite element error estimates are shown and the validity of these results is confirmed by numerical experiments.
Cite
@article{arxiv.1901.03612,
title = {Error estimates for the finite element approximation of bilinear boundary control problems},
author = {Max Winkler},
journal= {arXiv preprint arXiv:1901.03612},
year = {2024}
}
Comments
39 pages, 1 figure