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.
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Ito, K., Ravindran, S.S. (1998). A Reduced Basis Method for Control Problems Governed by PDEs. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems. International Series of Numerical Mathematics, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8849-3_12
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DOI: https://doi.org/10.1007/978-3-0348-8849-3_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9800-3
Online ISBN: 978-3-0348-8849-3
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