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The Output Least Squares Identifiability of the Diffusion Coefficient from an H1–Observationin a 2–D Elliptic Equation

Published online by Cambridge University Press:  15 August 2002

Guy Chavent  and
Karl Kunisch
Guy Chavent
Affiliation:
Ceremade, Université Paris–Dauphine, Paris Cedex 16, France; guy.chavent@inria.fr.
Karl Kunisch
Affiliation:
Institute of Mathematics, University of Graz, Austria.
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Abstract

Output least squares stability for the diffusion coefficient in an elliptic equation in dimensiontwo is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability.The analysis shows the influence of the flow direction on the parameter to be estimated.A scale analysis for multi-scale resolution of the unknown parameter is provided.

Keywords

Parameter estimationdiffusion coefficientinverse problemidentifiabilityleast squares.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 423 - 440
Copyright
© EDP Sciences, SMAI, 2002

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