Amit Apte, Didier Auroux, Mythily Ramaswamy
Abstract:
We present an optimal control formulation of the data assimilation
problem for the Burgers' equation, with the initial condition as the
control. First the convergence of the implicit Lax-Friedrichs
numerical discretization scheme is presented. Then we study the
dependence of the convergence of the associated minimization problem
on different terms in the cost function, specifically, the weight for
the regularization and the number of observations, as well as the
a priori approximation of the initial condition. We present
numerical evidence for multiple minima of the cost function without
regularization, while only a single minimum is seen for the
regularized problem.
Published September 25, 2010.
Math Subject Classifications: 35L03.
Key Words: Variational data assimilation; Burgers equation;
Lax-Friedrichs scheme.
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Amit Apte TIFR Center for Applicable mathematics, Post Bag No. 6503 Chikkabommasandra, Bangalore 560065 India email: apte@math.tifrbng.res.in |
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Didier Auroux Laboratoire J.-A. Dieudonne, Universite de Nice Sophia Antipolis, Parc Valrose, F-06108 Nice cedex 2, France email: auroux@unice.fr |
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Mythily Ramaswamy TIFR Center for Applicable mathematics, Post Bag No. 6503 Chikkabommasandra, Bangalore 560065 India email: mythily@math.tifrbng.res.in |
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