Multigoal-oriented optimal control problems with nonlinear PDE constraints

被引：4

作者：

Endtmayer, B. ^{[1
,2
]}

Langer, U. ^{[1
]}

Neitzel, I ^{[3
]}

Wick, T. ^{[4
,5
]}

Wollner, W. ^{[6
]}

机构：

[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, Altenbergerstr 69, A-4040 Linz, Austria

[2] Johannes Kepler Univ Linz, Doctoral Program Computat Math, Altenbergerstr 69, A-4040 Linz, Austria

[3] Inst Numer Simulat, Endenicher Allee 19b, D-53115 Bonn, Germany

[4] Leibniz Univ Hannover, Inst Angew Math, AG Wissensch Rechnen, Welfengarten 1, D-30167 Hannover, Germany

[5] Leibniz Univ Hannover, Cluster Excellence PhoenixD Photon Opt & Engn Inn, Hannover, Germany

[6] Tech Univ Darmstadt, Fachbereich Math, Dolivostr 15, D-64293 Darmstadt, Germany

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 79卷 / 10期

基金：

奥地利科学基金会;

关键词：

Optimal control; Multigoal-oriented a posteriori error estimation; Regularized p-Laplacian; Dual-weighted residuals; Finite elements; POSTERIORI ERROR ESTIMATION; FINITE-ELEMENT METHODS; P-LAPLACIAN; APPROXIMATION; ALGORITHM; ADAPTIVITY;

D O I：

10.1016/j.camwa.2020.01.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页码：3001 / 3026

页数：26

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