A posteriori error estimates for distributed convex optimal control problems. (English) Zbl 1008.49024

Liu, Wenbin; Yan, Ningning

Adv. Comput. Math. 15, No. 1-4, 285-309 (2001).

The authors consider the following distributed convex optimal control problem \[ \min_{u\in C} \{g(y)+ h(u)\},\quad -\text{div}(A\nabla y)= f+ Bu\quad\text{in }\Omega,\quad y|_{\partial\Omega}= 0. \] For this problem, an a posteriori error analysis for finite element approximation is given. Explicit estimates are presented for some model problems which appear in real-life applications.

Reviewer: Hans Benker (Merseburg)

MSC:

49M25	Discrete approximations in optimal control
49J20	Existence theories for optimal control problems involving partial differential equations
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

distributed convex optimal control problem; error analysis; finite element approximation