Mixed Finite Element Method for Dirichlet Boundary Control Problem Governed by Elliptic PDEs

Finite Element Method for Constrained Optimal Control Problems Governed by Nonlinear Elliptic Pdes

In this paper, we study the finite element method for constrained optimal control problems governed by nonlinear elliptic PDEs. Instead of the standard error estimates under L2or H1norm, we apply the goal-oriented error estimates in order to avoid the difficulties which are generated by the nonsmoothness of the problem. We derive the a priori error estimates of the goal function, and the error ...

Finite Element Approximation of Dirichlet Boundary Control for Elliptic PDEs on Two- and Three-Dimensional Curved Domains

We consider the variational discretization of elliptic Dirichlet optimal control problems with constraints on the control. The underlying state equation, which is considered on smooth twoand three-dimensional domains, is discretized by linear finite elements taking into account domain approximation. The control variable is not discretized. We obtain optimal error bounds for the optimal control ...

The Finite Element Method for 2D elliptic PDEs

THE h × p FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEMS CONSTRAINED BY STOCHASTIC ELLIPTIC PDES

This paper analyzes the h × p version of the finite element method for optimal control problems constrained by elliptic partial differential equations with random inputs. The main result is that the h × p error bound for the control problems subject to stochastic partial differential equations leads to an exponential rate of convergence with respect to p as for the corresponding direct problems...

Adaptive Finite Element Method for Optimal Control Problem Governed by Linear Quasiparabolic Integrodifferential Equations

and Applied Analysis 3 We are interested in the following optimal control problem: min u∈Uad⊂X J ( u, y u ) 1 2 {∫T 0 ∥ ∥y − zd ∥ ∥2 0,Ωdt ∫T 0 ‖u‖0,ΩUdt } , 2.1 subject to yt − div ( A∇yt D∇y ∫ t 0 C t, τ ∇y x, τ dτ ) f Bu, in Ω × 0, T , y 0, on ∂Ω × 0, T , y|t 0 y0, in Ω, 2.2 where u is control, y is state, zd is the observation, Uad is a closed convex subset, f x, t ∈ L2 0, T ;L2 Ω , and zd ...