Volume 10, Issue 1
Equivalent a Posteriori Error Estimates for a Constrained Optimal Control Problem Governed by Parabolic Equations

Tongjun Sun, Liang Ge & WenbinLiu


Int. J. Numer. Anal. Mod., 10 (2013), pp. 1-23.

Published online: 2013-10

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  • Abstract

In this paper, we study adaptive finite element approximation in the backward Euler scheme for a constrained optimal control problem by parabolic e- quations on multi-meshes. The control constraint is given in an integral sense: K = {u(t) ∈ L^2( Ω) : a ≤ ∫_ Ω u(t) ≤ b}. We derive equivalent a posteriori error estimates with lower and upper bounds for both the state and the control approxi- mation, which are used as indicators in adaptive multi-meshes finite element scheme. The error estimates are then implemented and tested with promising numerical ex- periments.

  • Keywords

constrained optimal control problem adaptive finite element approxi-mation equivalent a posteriori error estimates parabolic equations multi-meshes

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