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A Posteriori Error Estimates for Convex Boundary Control Problems

Authors:

Wenbin Liu,

Ningning YanAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 39, Issue 1

Pages 73 - 99

https://doi.org/10.1137/S0036142999352187

Published: 01 January 2001 Publication History

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Abstract

In this paper, we present an a posteriori error analysis for the finite element approximation of convex optimal Neumann boundary control problems. We derive a posteriori error estimates for both the state and the control approximation, first on polygonal domains and then on Lipschitz piecewise C² domains. Such estimates, which are apparently not available in the literature, can be used to construct reliable adaptive finite element approximation schemes for the control problems. Explicit estimates are shown for some model problems that frequently appear in applications.

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Manohar R(2024)Error analysis for finite element approximation of parabolic Neumann boundary control problemsComputers & Mathematics with Applications10.1016/j.camwa.2024.01.004158:C(102-117)Online publication date: 15-Mar-2024
https://dl.acm.org/doi/10.1016/j.camwa.2024.01.004
Wang FWang QZhou Z(2024)Adaptive finite element approximation of bilinear optimal control problem with fractional LaplacianCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-024-00611-261:4Online publication date: 1-Nov-2024
https://dl.acm.org/doi/10.1007/s10092-024-00611-2
Garg DPorwal K(2023)Unified discontinuous Galerkin finite element methods for second order Dirichlet boundary control problemApplied Numerical Mathematics10.1016/j.apnum.2022.12.001185:C(336-364)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.apnum.2022.12.001
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A Posteriori Error Estimates for Convex Boundary Control Problems
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
    2. Numerical analysis

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cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 39, Issue 1

2001

362 pages

ISSN:0036-1429

Issue’s Table of Contents

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2001

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Manohar R(2024)Error analysis for finite element approximation of parabolic Neumann boundary control problemsComputers & Mathematics with Applications10.1016/j.camwa.2024.01.004158:C(102-117)Online publication date: 15-Mar-2024
https://dl.acm.org/doi/10.1016/j.camwa.2024.01.004
Wang FWang QZhou Z(2024)Adaptive finite element approximation of bilinear optimal control problem with fractional LaplacianCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-024-00611-261:4Online publication date: 1-Nov-2024
https://dl.acm.org/doi/10.1007/s10092-024-00611-2
Garg DPorwal K(2023)Unified discontinuous Galerkin finite element methods for second order Dirichlet boundary control problemApplied Numerical Mathematics10.1016/j.apnum.2022.12.001185:C(336-364)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.apnum.2022.12.001
Zhou ZWang Q(2023)Adaptive finite element approximation of optimal control problems with the integral fractional LaplacianAdvances in Computational Mathematics10.1007/s10444-023-10064-w49:4Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1007/s10444-023-10064-w
Shen YGong WYan N(2022)Convergence of adaptive nonconforming finite element method for Stokes optimal control problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114336412:COnline publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1016/j.cam.2022.114336
Manohar RSinha R(2022)Local a posteriori error estimates for boundary control problems governed by nonlinear parabolic equationsJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114146409:COnline publication date: 1-Aug-2022
https://dl.acm.org/doi/10.1016/j.cam.2022.114146
Manohar RSinha R(2022)Local a Posteriori Error Analysis of Finite Element Method for Parabolic Boundary Control ProblemsJournal of Scientific Computing10.1007/s10915-022-01788-w91:1Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s10915-022-01788-w
Feng MSun T(2022)A priori error estimate of perturbation method for optimal control problem governed by elliptic PDEs with small uncertaintiesComputational Optimization and Applications10.1007/s10589-022-00352-481:3(889-921)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s10589-022-00352-4
Leng HChen Y(2021)Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problemsAdvances in Computational Mathematics10.1007/s10444-021-09864-947:3Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s10444-021-09864-9
Shen YYan NZhou Z(2019)Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problemJournal of Computational and Applied Mathematics10.1016/j.cam.2019.01.038356:C(1-21)Online publication date: 15-Aug-2019
https://dl.acm.org/doi/10.1016/j.cam.2019.01.038
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