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Numerical Approximation of a Control Problem for Advection-Diffusion Processes

  • A. Quarteroni
  • G. Rozza
  • L. Dedè
  • A. Quaini
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 199)

Abstract

Two different approaches are proposed to enhance the efficiency of the numerical resolution of optimal control problems governed by a linear advection-diffusion equation. In the framework of the Galerkin-Finite Element (FE) method, we adopt a novel a posteriori error estimate of the discretization error on the cost functional; this estimate is used in the course of a numerical adaptive strategy for the generation of efficient grids for the resolution of the optimal control problem. Moreover, we propose to solve the control problem by adopting a reduced basis (RB) technique, hence ensuring rapid, reliable and repeated evaluations of input-output relationship. Our numerical tests show that by this technique a substantial saving of computational costs can be achieved.

keywords

optimal control problems partial differential equations finite element approximation reduced basis techniques advection-diffusion equations stabilized Lagrangian numerical adaptivity 

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Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • A. Quarteroni
    • 1
    • 2
  • G. Rozza
    • 1
  • L. Dedè
    • 2
  • A. Quaini
    • 1
  1. 1.FSB, Chaire de Modelisation et Calcul Scientifique (CMCS)École Polytechnique Fédérate de Lausanne (EPFL)LausanneSwitzerland
  2. 2.MOX-Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilanoItaly

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