Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation

Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation

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 e...

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Veröffentlicht in:IMA journal of numerical analysis 2021-10, Vol.41 (4), p.2639-2667
Hauptverfasser: Engel, Sebastian, Vexler, Boris, Trautmann, Philip
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Vexler, Boris
Trautmann, Philip
description 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.
doi_str_mv 10.1093/imanum/draa032
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source Oxford University Press Journals All Titles (1996-Current)
title Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation
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