The Output Least Squares Identifiability of the Diffusion Coefficient from an H1–Observation in a 2–D Elliptic Equation
Université Paris–Dauphine, Paris Cedex 16, France; firstname.lastname@example.org.
2 Institute of Mathematics, University of Graz, Austria.
Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two 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.
Mathematics Subject Classification: 62G05 / 35R30 / 93E24
Key words: Parameter estimation / diffusion coefficient / inverse problem / identifiability / least squares.
© EDP Sciences, SMAI, 2002