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Boundary concentrated finite elements for optimal control problems with distributed observation

Author

Listed:
  • S. Beuchler
  • K. Hofer
  • D. Wachsmuth
  • J.-E. Wurst

Abstract

We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. If the constraint is a $$H^{1+\delta }(\Omega )$$ H 1 + δ ( Ω ) regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case that the discretization error in the $$L_2$$ L 2 norm decreases like $$N^{-\delta }$$ N - δ , where $$N$$ N is the number of unknowns. Our approach is suitable for solving a wide class of problems, among them piecewise defined data and tracking functionals acting only on a subdomain of $$\Omega $$ Ω . We present several numerical results. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • S. Beuchler & K. Hofer & D. Wachsmuth & J.-E. Wurst, 2015. "Boundary concentrated finite elements for optimal control problems with distributed observation," Computational Optimization and Applications, Springer, vol. 62(1), pages 31-65, September.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:1:p:31-65
    DOI: 10.1007/s10589-015-9737-5
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    References listed on IDEAS

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    1. Thomas Apel & Johannes Pfefferer & Arnd Rösch, 2012. "Finite element error estimates for Neumann boundary control problems on graded meshes," Computational Optimization and Applications, Springer, vol. 52(1), pages 3-28, May.
    2. Sven Beuchler & Clemens Pechstein & Daniel Wachsmuth, 2012. "Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs," Computational Optimization and Applications, Springer, vol. 51(2), pages 883-908, March.
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