Eighth Mississippi State  UAB Conference on Differential Equations
and Computational Simulations.
Electron. J. Diff. Eqns., Conference 19 (2010), pp. 1530.
Variational data assimilation for discrete Burgers equation
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 LaxFriedrichs
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;
LaxFriedrichs 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


Didier Auroux
Laboratoire J.A. Dieudonne, Universite de Nice Sophia
Antipolis, Parc Valrose, F06108 Nice cedex 2, France
email: auroux@unice.fr


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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