A Priori Error Analysis for an Optimal Control Problem Governed by a\n Variational Inequality of the Second Kind

2020/11/24 by Christian Meyer, Meyer, Christian, Monika Weymuth +1
Computer Science · Engineering · #49M25 #65G99 #65K15 #65N30 #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2011.12199

openalex publication_date 2020/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an optimal control problem governed by an elliptic variational\ninequality of the second kind. The problem is discretized by linear finite\nelements for the state and a variational discrete approach for the control.\nBased on a quadratic growth condition we derive nearly optimal a priori error\nestimates. Moreover, we establish second order sufficient optimality conditions\nthat ensure a quadratic growth condition. These conditions are rather\nrestrictive, but allow us to construct a one-dimensional locally optimal\nsolution with reduced regularity, which serves as an exact solution for\nnumerical experiments.\n

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