A Priori Error Analysis for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind. (2nd January 2022)

• Record Type: Journal Article
• Authors: Meyer, C.; Weymuth, M.
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 1(2022)
• Page Start: 35
• Page End: 67
• Publication Date: 2022-01-02
• Subjects: A priori error analysis -- elliptic variational inequalities of the second kind -- finite elements -- optimal control; 49M25 -- 65G99 -- 65K15 -- 65N30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2001750
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a quadratic growth condition we derive nearly optimal a priori error estimates. Moreover, we establish second order sufficient optimality conditions that ensure a quadratic growth condition. These conditions are rather restrictive, but allow us to construct a one-dimensional locally optimal solution with reduced regularity, which serves as an exact solution for numerical experiments.