In this paper we consider one-dimensional flow governed by Burgers' equation. We analyze two iterative methods for data assimilation problem for this equation. One of them so called adjoint optimization method, is based on minimization in L 2-norm. We show that this minimization problem is ill-posed but the adjoint optimization iterative method is regularizing, and represents the well-known Landweber method in inverse problems. The second method is based on L 2-minimization of the gradient. We prove that this problem always has a solution. We present numerical comparisons of these two methods.
Editor-in-Chief: Kabanikhin, Sergey I.
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Iterative methods for data assimilation for Burgers' equation
∗Department of Mathematics, Linköpings Universitet, SE-581 83 Linköping, Sweden. E-mails: johlu@mai.liu.se, vlkoz@mai.liu.se
†Aeronautical Engineering, Saab Aerosystems, SE-581 88 Linköping, Sweden. E-mail: per.weinerfelt@saab.se
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 5, Pages 505–535, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406778247589,
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