A posteriori error estimation of finite element approximations of pointwise state constrained distributed control problems

A posteriori error estimation of finite element approximations of pointwise state constrained distributed control problems

We provide an a posteriori error analysis of finite element approximations of pointwise state constrained distributed optimal control problems for second order elliptic boundary value problems. In particular, we derive a residual-type a posteriori error estimator and prove its efficiency and reliability up to oscillations in the data of the problem and a consistency error term. In contrast to t...

Adaptive Finite Elements for State-Constrained Optimal Control Problems - Convergence Analysis and A Posteriori Error Estimation

A Posteriori Finite Element Error Estimation for Diffusion Problems

Adjerid et al. 2] and Yu 19, 20] show that a posteriori estimates of spatial discretiza-tion errors of piecewise bi-p polynomial nite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even. We show that these simple error esti...

Localized pointwise a posteriori error estimates for gradients of piecewise linear finite element approximations to second-order quasilinear elliptic problems

Two types of pointwise a posteriori error estimates are presented for gradients of finite element approximations of second-order quasilinear elliptic Dirichlet boundary value problems over convex polyhedral domains Ω in space dimension n ≥ 2. We first give a residual estimator which is equivalent to ‖∇(u − uh)‖L∞(Ω) up to higher-order terms. The second type of residual estimator is designed to ...

Reliable a posteriori error estimation for state-constrained optimal control

We derive a reliable a posteriori error estimator for a state-constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both discretised and non-discretised control. The performance of our estimator is illustrated by several numerical examples for which we also introd...