A Reduced Basis Method for Control Problems Governed by PDEs

  • K. Ito
  • S. S. Ravindran
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 126)

Abstract

This article presents a reduced basis method for constructing a reduced order system for control problems governed by nonlinear partial differential equations. The major advantage of the reduced basis method over others based on finite element, finite difference or spectral method is that it may capture the essential property of solutions with very few basis elements. The feasibility of this method is demonstrated for boundary control problems modeled by the incompressible Navier-Stokes and related equations with the boundary temperature control and boundary electromagnetic control in channel flows.

1991 Mathematics Subject Classification

93B40 49M05 76D05 49K20 65H10 76W05 80A20 

Key words and phrases

Reduced basis method finite elements optimal control flow control boundary temperature control electromagnetic control 

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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • K. Ito
    • 1
  • S. S. Ravindran
    • 1
  1. 1.Center for Research in Scientific Computation Department of MathematicsNorth Carolina State UniversityRaleighUSA

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