Sharp a posteriori error estimates for optimal control governed by parabolic integro-differential equations

DOI10.1007/s10915-014-9957-3zbMath1331.65090OpenAlexW2012061381MaRDI QIDQ898411

Danping Yang, Liang Ge, Wan-fang Shen, Wen-bin Liu

Publication date: 9 December 2015

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-014-9957-3

zbMATH Keywords

optimal controlnumerical resultsa posteriori error estimatesmaterials with memoryparabolic integro-differential equationsadaptive finite elementselastic-plastic mechanicsheat conduction controlpopulation dynamics control

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Population dynamics (general) (92D25) Heat equation (35K05) Discrete approximations in optimal control (49M25) Existence theories for optimal control problems involving relations other than differential equations (49J21)

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A priori error estimates and superconvergence of splitting positive definite mixed finite element methods for pseudo-hyperbolic integro-differential optimal control problems ⋮ A Sparse Grid Stochastic Collocation Discontinuous Galerkin Method for Constrained Optimal Control Problem Governed by Random Convection Dominated Diffusion Equations ⋮ New elliptic projections and a priori error estimates of \(H^1\)-Galerkin mixed finite element methods for optimal control problems governed by parabolic integro-differential equations ⋮ A priori and a posteriori error estimates of \(H^1\)-Galerkin mixed finite element methods for optimal control problems governed by pseudo-hyperbolic integro-differential equations ⋮ Full-discrete adaptive FEM for quasi-parabolic integro-differential PDE-constrained optimal control problem ⋮ An optimal indirect control of underwater vehicle ⋮ Approximate controllability of linear parabolic equation with memory

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