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Rate of Convergence for Eigenfunctions of Aharonov-Bohm Operators with a Moving Pole Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Optimal A Priori Error Estimates of Parabolic Optimal Control Problems with a Moving Point Control

Authors : Dmitriy Leykekhman, Boris Vexler

Published in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Publisher: Springer International Publishing

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Abstract

In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear finite elements in space. For this discretization we show optimal order of convergence with respect to the time and the space discretization parameters modulo some logarithmic terms. Error analysis for the same problem was carried out in the recent paper (Gong and Yan, SIAM J Numer Anal 54:1229–1262, 2016), however, the analysis there contains a serious flaw. One of the main goals of this paper is to provide the correct proof. The main ingredients of our analysis are the global and local error estimates on a curve, that have an independent interest.

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previous chapter Boundedness of Solutions to a Degenerate Diffusion Equation
next chapter A Note on the Feedback Stabilization of a Cahn–Hilliard Type System with a Singular Logarithmic Potential
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Metadata
Title
Optimal A Priori Error Estimates of Parabolic Optimal Control Problems with a Moving Point Control
Authors
Dmitriy Leykekhman
Boris Vexler
Copyright Year
2017
Book
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Print ISBN: 978-3-319-64488-2

Electronic ISBN: 978-3-319-64489-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-64489-9_13

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