Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 19 (2010), pp. 15-30.

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 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.

Show me the PDF file (836K), TEX file, and other files for this article.

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, F-06108 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

Return to the table of contents for this conference.
Return to the EJDE web page