A posteriori error estimates for control problems governed by nonlinear elliptic equations

Authors:
Wenbin Liu;Ningning Yan
Affiliations:
CBS & IMS, University of Kent, Canterbury, CT2 7NF, UK;Institute of System Sciences, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Year:
2003

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Abstract

In this paper, we derive a posteriori error estimates for the finite element approximation of a class of nonlinear optimal control problems. We derive a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, can be used to construct reliable adaptive finite element approximation schemes for the control problems.