A posteriori error estimates for optimal distributed control governed by the evolution equations

Authors:
Chunguang Xiong;Yuan Li
Affiliations:
Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China;Department of Mathematics, Chinese People's Armed Police Forces Academy, Hebei, 065000, China
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

We describe a technique for a posteriori error estimates suitable to the optimal control problem governed by the evolution equations solved by the method of lines. It is applied to the control problem governed by the parabolic equation, convection-diffusion equation and hyperbolic equation. The error is measured with the aid of the L^2-norm in the space-time cylinder combined with a special time weighted energy norm.