Multigoal-oriented optimal control problems with nonlinear PDE constraints

verfasst von

B. Endtmayer, U. Langer, I. Neitzel, T. Wick, W. Wollner

Abstract

In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to a semi-linear monotone PDE and the regularized p-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is formulated. Based on the reduced approach, we then derive an a posteriori error representation and mesh adaptivity for multiple quantities of interest. All quantities are combined to one, and then the dual-weighted residual (DWR) method is applied to this combined functional. Furthermore, the estimator allows for balancing the discretization error and the nonlinear iteration error. These developments allow us to formulate an adaptive solution strategy, which is finally substantiated with the help of several numerical examples.

Organisationseinheit(en)

Institut für Angewandte Mathematik
PhoenixD: Simulation, Fabrikation und Anwendung optischer Systeme

Externe Organisation(en)

Austrian Academy of Sciences
Johannes Kepler Universität Linz (JKU)
Technische Universität Darmstadt
Rheinische Friedrich-Wilhelms-Universität Bonn

Typ

Artikel

Journal

Computers and Mathematics with Applications

Band

79

Seiten

3001-3026

Anzahl der Seiten

26

ISSN

0898-1221

Publikationsdatum

15.05.2020

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Modellierung und Simulation, Theoretische Informatik und Mathematik, Computational Mathematics

Elektronische Version(en)

https://doi.org/10.48550/arXiv.1903.02799 (Zugang: Offen)
https://doi.org/10.1016/j.camwa.2020.01.005 (Zugang: Geschlossen)