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Solvability and numerical algorithms for a class ofvariational dataassimilation problems

Published online by Cambridge University Press:  15 August 2002

Guri Marchuk  and
Victor Shutyaev
Guri Marchuk
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 GSP-1 Russia; shutyaev@inm.ras.ru.
Victor Shutyaev
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 GSP-1 Russia; shutyaev@inm.ras.ru.
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Abstract

A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.

Keywords

Variational data assimilationquasilinear evolution problemoptimality systemcontrol equationsolvabilityiterative algorithms.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 873 - 883
Copyright
© EDP Sciences, SMAI, 2002

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