Multigoal-oriented optimal control problems with nonlinear PDE constraints

authored by

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.

Organisation(s)

Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines

External Organisation(s)

Austrian Academy of Sciences
Johannes Kepler University of Linz (JKU)
Technische Universität Darmstadt
University of Bonn

Type

Article

Journal

Computers and Mathematics with Applications

Volume

79

Pages

3001-3026

No. of pages

26

ISSN

0898-1221

Publication date

15.05.2020

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Modelling and Simulation, Computational Theory and Mathematics, Computational Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.1903.02799 (Access: Open)
https://doi.org/10.1016/j.camwa.2020.01.005 (Access: Closed)