Optimal Control Problems Governed by Elliptic Variational Inequalities

Optimal Control Problems Governed by Elliptic Variational Inequalities

 Supervision: 

• Prof. Thomas Apel

Development:  

• Christof Haubner
• Dr. sc. nat. Monika Weymuth (2017-2020)

 Goals: 

• A priori error analysis for finite element discretizations of optimal control problems governed by variational inequalities
• Analysis of different regularization techniques with a focus on investigating the regularization and discretization errors
• Development and analysis of non-smooth optimization methods

• Verification of the theoretical results by numerical tests

 Publications related to the project: 

• O. Weiß, M. Weymuth: On Solving Elliptic Obstacle Problems by Compact Abs-Linearization [ Preprint ]
• C. Meyer, M. Weymuth: A Priori Error Analysis for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind. Numerical Functional Analysis and Optimization, DOI: 10.1080/01630563.2021.2001750
• C. Christof, C. Haubner: Finite element error estimates in non-energy norms for the two-dimensional scalar Signorini problem. Numer. Math 145, 2020 [Paper]
• T. Apel, S. Nicaise: Regularity of the solution of the scalar Signorini problem in polygonal domains. Results Math. 75, 2020 [Preprint] / [Paper]
• C. Meyer, M. Weymuth: A Priori Error Estimates for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind. PAMM Proc. Appl. Math. Mech. 19, 2019. [PDF]