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Numerical Algorithms

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11.01.2022 | Original Paper

A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem

verfasst von: Qiming Wang, Zhaojie Zhou

Erschienen in: Numerical Algorithms | Ausgabe 3/2022

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Abstract

In this paper, a virtual element method (VEM) discretization of elliptic optimal control problem with pointwise control constraint is investigated. Virtual element discrete scheme is constructed based on virtual element approximation of the state equation and variational discretization of the control variable. A priori error estimates for state, adjoint state and control variable in H¹ and L² norms are derived. Due to the attractive flexibility of VEM in dealing with mesh refinement we also derive a posteriori error estimates for the optimal control problem, which are used to guide the mesh refinement in the adaptive VEM algorithm. Numerical experiments are carried out to illustrate the theoretical findings.

Vorheriger Artikel Completely discrete schemes for 2D Sobolev equations with Burgers’ type nonlinearity

Nächster Artikel A modified conjugate gradient method based on the self-scaling memoryless BFGS update

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Titel: A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem
verfasst von: Qiming Wang
Zhaojie Zhou
Publikationsdatum: 11.01.2022
Verlag: Springer US
Erschienen in: Numerical Algorithms / Ausgabe 3/2022
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-021-01219-1

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