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A Quadratic C0 Interior Penalty Method for an Elliptic Optimal Control Problem with State Constraints

  • S. C. Brenner
  • L.-Y. Sung
  • Y. ZhangEmail author
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 157)

Abstract

We consider an elliptic distributed optimal control problem on convex polygonal domains with pointwise state constraints and solve it as a fourth order variational inequality for the state by a quadratic C 0 interior penalty method. The error for the state in an H 2-like energy norm is O(h α ) on quasi-uniform meshes (where α ∈ (0, 1] is determined by the interior angles of the domain) and O(h) on graded meshes. The error for the control in the L 2 norm has the same behavior. Numerical results that illustrate the performance of the method are also presented.

Keywords

Elliptic distributed optimal control problem Pointwise state constraints Simply supported plate Fourth order variational inequality Finite element C0 interior penalty method Discontinuous Galerkin Graded meshes 

Notes

Acknowledgements

The authors would like to thank an anonymous referee for suggesting the piecewise quadratic approximation of the optimal control defined by (5.11). The work of S.C. Brenner, L.-Y. Sung, and Y. Zhang was supported in part by the National Science Foundation under Grant No. DMS-10-16332.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Mathematics and Center for Computation and TechnologyLouisiana State UniversityBaton RougeUSA

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