Iterative Methods for Data Assimilation for Burgers's Equation
2006 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219 (print, 1569-3945 (online), Vol. 14, no 5, 505-535 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2006. Vol. 14, no 5, 505-535 p.
IdentifiersURN: urn:nbn:se:liu:diva-14646DOI: 10.1515/156939406778247589OAI: oai:DiVA.org:liu-14646DiVA: diva2:24088