[PDF] Top 20 A posteriori error estimates for the fractional optimal control problems

... Riemann-Liouville fractional integration were introduced in [] to solve a general class of FOCP, and the convergence of the proposed method was also extensively ...Caputo fractional derivative, and a ... See full document

... priori error estimates will be established in two ...the control space is given implicitly by the necessary optimality ...the control space. Here, we require a regularity result on the ... See full document

... a posteriori error indicator. A posteriori error estimates are computable quan- tities in terms of the discrete solution that measure the actual discrete errors without the knowledge of ... See full document

... The optimal control of VIs (with the standard objective functional contain- ing an L 2 (Ω)-fidelity term, as in Chapter 1) has been well studied in both the finite dimensional case [Luo et ...the ... See full document

... a posteriori error estimator to drive AFEMs. Our error indicator is built on the basis of the error estimator for elliptic problems involving Dirac measures elaborated in [1] and the ... See full document

... many control problems, the objective functional contains gradient of the state ...mal control problems, mixed finite element methods are not widely used in engineer- ing ...of optimal ... See full document

... PDE-constrained optimal control problems (OCPs), such as elliptic, parabolic, and hyperbolic equation constrained ...trol problems in many practical applications, as far as we know, there has ... See full document

... the optimal control problems and its mixed finite element ...a posteriori estimates for the fourth order hyperbolic optimal control problems in ... See full document

... priori error estimates are to be validated for the error in the control, state, and co- ...the control function u is not discretized, whereas the state ( p  , y ) and the co-state ( q ... See full document

... the error analysis in the maximum norm for a class of nonlinear elliptic problems in the context of overlapping nonmatching grids and they established the optimal L ∞ -error estimate between ... See full document

... a posteriori error indicators can be used to select meshes that are quasi-optimal for both the deformation gradient and for the ...sharper estimates on actual errors (in particular the energy ... See full document

... a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) ...example problems: one where the oral ... See full document

... hyperbolic optimal control ...a posteriori error estimates and superconvergence of mixed finite element solution for fourth order hyperbolic optimal control ... See full document

... optimal control problems (see, e.g., [–]). Although bilinear optimal control problems are frequently met in applications, they are much more difficult to handle in comparison to ... See full document

... a posteriori error estimates for the spectral ap- proximation of an optimal control problem governed by nonlinear parabolic ...a posteriori error estimates of the ... See full document

... In many application, S(·) is uniform convex near the solution u. The convexity of S(·) is closely related to the second order sufficient conditions of the optimal control problems, which are assumed in ... See full document

... Recently, the adaptive finite element method has been investigated extensively. It has become one of the most popular methods in the scientific computation and numerical modeling. An adaptive finite element approximation ... See full document

... Optimal control problems have been successfully utilized in scientific and engineering numerical ...of optimal control ...for optimal control problems can be found ... See full document

... the optimal control problems governed by integro-differential equations and briefly state the definitions and properties of some interpolation ...a posteriori error estimates for ... See full document

... convex optimal control problems where the control appears in the Neumann boundary ...boundary optimal control problems, we have to give a weak formula for the state ... See full document