Adaptive finite element method for an unregularized semilinear optimal control problem

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational discretization approach. For this solution technique, we design an a po...

Full description

Saved in:
Bibliographic Details
Main Authors Fuica, Francisco, Jork, Nicolai
Format Journal Article
LanguageEnglish
Published 07.05.2025
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Mathematics - Optimization and Control
Online AccessGet full text
DOI10.48550/arxiv.2505.04439

Cover

More Information
Summary:We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational discretization approach. For this solution technique, we design an a posteriori error estimator that accounts for the discretization of the state and adjoint equations, and prove, under suitable local growth conditions of optimal controls, reliability and efficiency properties of such error estimator. A simple adaptive strategy based on the devised estimator is designed and its performance is illustrated with numerical examples.
DOI:10.48550/arxiv.2505.04439