Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation. (27th July 2020)

• Record Type: Journal Article
• Authors: Engel, Sebastian; Vexler, Boris; Trautmann, Philip
• Is Part Of: IMA journal of numerical analysis. Volume 41:Number 4(2021)
• Page Start: 2639
• Page End: 2667
• Publication Date: 2020-07-27
• Subjects: optimal control problems involving partial differential equations -- wave equation -- functions of bounded variation -- discrete approximations -- error bounds -- finite elements; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/draa032
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization method. The state equation is discretized by a space-time finite element method. The controls are not discretized. Under suitable assumptions optimal convergence rates for the error in the state and control variable are proven. Based on a conditional gradient method the solution of the semi-discretized optimal control problem is computed. The theoretical convergence rates are confirmed in a numerical example.