A model-data weak formulation for simultaneous estimation of state and model bias
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Patera_A model-data.pdf
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Author(s)
Yano, Masayuki
Penn, James Douglass
Patera, Anthony T.
Alternative Title
A model-data weak formulation for simultaneous estimation of state and model bias Estimation de la variable dʼétat et du biais de modèle par une formulation faible incorporant les données
Date Issued
November 2013
Journal
Comptes Rendus Mathematique
Publisher
Elsevier
Citation
Yano, Masayuki, James D. Penn, and Anthony T. Patera. “A Model-Data Weak Formulation for Simultaneous Estimation of State and Model Bias.” Comptes Rendus Mathematique 351, no. 23–24 (December 2013): 937–941.
Version
Original manuscript
Abstract
We introduce a Petrov–Galerkin regularized saddle approximation which incorporates a “model” (partial differential equation) and “data” (M experimental observations) to yield estimates for both state and model bias. We provide an a priori theory that identifies two distinct contributions to the reduction in the error in state as a function of the number of observations, M: the stability constant increases with M; the model-bias best-fit error decreases with M. We present results for a synthetic Helmholtz problem and an actual acoustics system.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.crma.2013.10.034
