Residual-based a posteriori error estimates for the hp version of the finite element discretization of the elliptic Robin boundary control problem

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AuteurGBEYA, SAMUEL
AuteurHOUEDANOU, KOFFI WILFRID
AuteurLEWIS, NYAGA
AuteurAHOUNOU, BERNARDIN
Date d'ajout2026-06-02T16:06:57Z
Date de disponibilite2026-06-02T16:06:57Z
Date de publication2022
ResumeOptimal control problems governed by partial differential equations have become a very active and successful research area. So, in this paper, we analyzed a priori and a posteriori error estimates for the hp finite element discretization of elliptic Robin boundary control problems. With the discrete and continuous optimality conditions of the problem, we constructed the error estimators. Based on the residual of the model equations for the coupled state and control approximations, the upper error bound is proved using Scott–Zhang-type quasi interpolation estimates. In order to provide the optimality, lower error bound is shown using some polynomial inverse estimates in weighted Sobolev spaces. Such estimators can be used to construct reliable adaptive methods for optimal control problems.
DOI10.1016/j.rinam.2022.100278
Autre identifiantBECDB-12543
URIhttps://dspace.uac.bj/handle/123456789/10822
Languefr
Fait partie deResults in Mathematics (Elsevier)
SujetOptimal control problems
Sujethp finite element method
SujetElliptic Robin boundary control problem
SujetA priori error estimates
SujetA posteriori error estimates of residual type
TitreResidual-based a posteriori error estimates for the hp version of the finite element discretization of the elliptic Robin boundary control problem
TypeArticle

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