Journal of Scientific Computing

, Volume 60, Issue 1, pp 160–183 | Cite as

Adaptive Finite Element Approximation for an Elliptic Optimal Control Problem with Both Pointwise and Integral Control Constraints

  • Ning Du
  • Liang Ge
  • Wenbin Liu


In this paper, we study the adaptive finite element approximation for a constrained optimal control problem with both pointwise and integral control constraints. We first obtain the explicit solutions for the variational inequalities both in the continuous and discrete cases. Then a priori error estimates are established, and furthermore equivalent a posteriori error estimators are derived for both the state and the control approximation, which can be used to guide the mesh refinement for an adaptive multi-mesh finite element scheme. The a posteriori error estimators are implemented and tested with promising numerical results.


Optimal control problem Finite element approximation  Adaptive finite element method A posteriori error estimates Multi-meshes 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina
  2. 2.Institute of Thermal Science and TechnologyShandong UniversityJinanChina
  3. 3.KBSUniversity of KentCanterburyUK

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