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

Chunguang Xiong; Yuan Li

doi:10.1016/j.apnum.2010.09.004

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

Chunguang Xiong^*, Yuan Li

^*Corresponding author for this work

School of Mathematics and Statistics

Chinese People's Police University

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

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 L2-norm in the space-time cylinder combined with a special time weighted energy norm.

Original language	English
Pages (from-to)	181-200
Number of pages	20
Journal	Applied Numerical Mathematics
Volume	61
Issue number	2
DOIs	https://doi.org/10.1016/j.apnum.2010.09.004
Publication status	Published - Feb 2011

Keywords

A posteriori error estimate
Evolution equation
FEM
Method of lines
Optimal control

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10.1016/j.apnum.2010.09.004

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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 L2-norm in the space-time cylinder combined with a special time weighted energy norm.",

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AB - 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 L2-norm in the space-time cylinder combined with a special time weighted energy norm.

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

Abstract

Keywords

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