Error estimates for a pointwise tracking optimal control problem of a semilinear elliptic equation
Numerical Analysis
2021-12-16 v2 Numerical Analysis
Optimization and Control
Abstract
We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. We devise two strategies of discretization to approximate a solution of the optimal control problem: a semidiscrete scheme where the control variable is not discretized -- the so-called variational discretization approach -- and a fully discrete scheme where the control variable is discretized with piecewise constant functions. For both solution techniques, we analyze convergence properties of discretizations and derive error estimates.
Cite
@article{arxiv.2009.00736,
title = {Error estimates for a pointwise tracking optimal control problem of a semilinear elliptic equation},
author = {Alejandro Allendes and Francisco Fuica and Enrique Otarola},
journal= {arXiv preprint arXiv:2009.00736},
year = {2021}
}