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A \(\varvec{C}^0\) Interior Penalty Method for Elliptic Distributed Optimal Control Problems in Three Dimensions with Pointwise State Constraints

  • Susanne C. BrennerEmail author
  • Minah Oh
  • Sara Pollock
  • Kamana Porwal
  • Mira Schedensack
  • Natasha S. Sharma
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 160)

Abstract

We investigate numerically a triquadratic \(C^0\) interior penalty method for elliptic distributed optimal control problems in three dimensions with pointwise state constraints, which is based on the formulation of these problems as fourth order variational inequalities. We obtain numerical results that are similar to the ones reported in [7, 8] for fourth order variational inequalities in two dimensions. The deal.II library [1, 2] is used for the numerical experiments.

Notes

Acknowledgments

The work of the first author was supported in part by the National Science Foundation under Grant No. DMS-13-19172.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Susanne C. Brenner
    • 1
    Email author
  • Minah Oh
    • 2
  • Sara Pollock
    • 3
  • Kamana Porwal
    • 1
  • Mira Schedensack
    • 4
  • Natasha S. Sharma
    • 5
  1. 1.Department of Mathematics and Center for Computation and TechnologyLouisiana State UniversityBaton RougeUSA
  2. 2.Department of Mathematics and StatisticsJames Madison UniversityHarrisonburgUSA
  3. 3.Department of MathematicsTexas A&M UniversityCollege StationUSA
  4. 4.Institut für Numerische SimulationUniversität BonnBonnGermany
  5. 5.Department of Mathematical SciencesUniversity of Texas of El PasoEl PasoUSA

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