[PDF] Top 20 A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state

... a priori error estimates will be established in two ...the state equation is discretized, e.g., the discretization of the control space is given implicitly by the necessary optimality ... See full document

... many control problems, the objective functional contains gradient of the state ...of gradient is important in numerical approximation of the state ...the state equations ... See full document

... of optimal control problems, the boundary optimal control is widely used in scientific and engineering ...boundary optimal control problems, Liu and Yan [, ] ... See full document

... a priori error estimates for nonlinear parabolic optimal control problems by mixed finite element ...posteriori error estimates of triangular mixed finite element ... See full document

... distributed optimal control problems governed by unsteady diffusion-convection- reaction equations with control ...fully-discrete state, adjoint and control and discuss the ... See full document

... many control problems, the objective functional contains the gradient of the state ...the gradient is important in numerical discretization of the coupled state ...the ... See full document

... diffusion problems may have boundary layers with small widths where their gradients change ...diffusion optimal control problems is generally not ...a priori knowledge of the locations of ... See full document

... an optimal control of Darcy flows, where the pri- mal state variable y means the pressure, the flux state variable σ stands for the velocity field, and the control variable u is an ... See full document

... a priori error estimates is investigated for variational discretization and mixed finite element methods of the semilinear parabolic optimal control problems with integral ...The ... See full document

... PDE optimal control problems with objective functionals that contain point evaluations of the ...such problems. [Tr¨ oltzsch, 2010] formulates an optimal control problem where ... 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

... 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

... displacement gradient in the U 1,2 - and U 1, ∞ -norms against the finite element mesh size ...deformation gradient of the solution, the effect of the mesh size is noticable for both ...the error ... See full document

... integro-differential optimal control problems. We derive a posteriori error estimates in L 2 (J;H 1 ( ))-norm and L 2 (J;L 2 ( ))-norm for both the coupled state and ... See full document

... In this section , we study the problem (P ) with the additional state constraint y ∈ K ⊂ H o 1 (Ω) closed convex subset. (3.1) By using a technique similar to the previous section we shall prove a result of ... See full document

... and pointwise error estimates, for Shepard operators on nonuniformly spaced meshes present a function depending on the mesh thickness at the ...case pointwise estimates as in [2, 4] are ... See full document

... solving optimal control problems with constraints is a reduction to auxiliary problems without restrictions with the help of Lagrangian functionals, on the basis of which the necessary ... See full document

... a priori information that models the source parameters can be used twice involving both the channel decoder and the source decoder for a better signal reconstruction [18, ... See full document

... of optimal control problem is ...model-based optimal control problem is discussed, where the adjusted parameters are added into the model ...modified optimal control problem, ... See full document

... is absolutely continuous. Without loss of generality, we normalize f such that F (1) = 1 and interpret F as a continuous probability distribution. Lastly, we assume that S(·, ·) is L×B-measurable, where L denotes the set ... See full document