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BIT Numerical Mathematics

, Volume 55, Issue 1, pp 255–277 | Cite as

Adaptive edge element approximation of H(curl)-elliptic optimal control problems with control constraints

  • Ronald H. W. HoppeEmail author
  • Irwin Yousept
Article

Abstract

A three-dimensional H(curl)-elliptic optimal control problem with distributed control and pointwise constraints on the control is considered. We present a residual-type a posteriori error analysis with respect to a curl-conforming edge element approximation of the optimal control problem. Here, the lowest order edge elements of Nédélec’s first family are used for the discretization of the state and the control with respect to an adaptively generated family of simplicial triangulations of the computational domain. In particular, the a posteriori error estimator consists of element and face residuals associated with the state equation and the adjoint state equation. The main results are the reliability of the estimator and its efficiency up to oscillations in terms of the data of the problem. In the last part of the paper, numerical results are included which illustrate the performance of the adaptive approach.

Keywords

Optimal control of PDEs H(curl)-elliptic problems Curl-conforming edge elements Residual a posteriori error estimator Reliability and efficiency 

Mathematics Subject Classification (2010)

49M05 65K10 65N30 65N50 78M10 

Notes

Acknowledgments

The first author acknowledges support by the NSF Grants DMS-1115658, DMS-1216857, by the German National Science Foundation within the Priority Programs SPP 1253, SPP 1506, by the German Federal Ministry for Education and Research (BMBF) within the projects BMBF-FROPT and BMBF-MeFreSim, and by the European Science Foundation (ESF) within the ESF Program OPTPDE.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Institute of MathematicsUniversity of AugsburgAugsburgGermany
  3. 3.Graduate School of Excellence Computational EngineeringTechnical University DarmstadtDarmstadtGermany

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