A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems -- Analysis, assessments and applications to parameter estimation

Abstract : We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder - in the construction procedure - and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the FitzHugh-Nagumo 1D model. Finally, we give detailed illustrations of the approach in two parameter estimation applications, the first in a variational estimation framework with the FitzHugh-Nagumo model, and the second with a beating heart mechanical model for which we employ a sequential estimation method to characterize model parameters using real image data in a clinical case.
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https://hal.inria.fr/hal-00834397
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Submitted on : Friday, June 14, 2013 - 6:51:27 PM
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Dominique Chapelle, Asven Gariah, Philippe Moireau, Jacques Sainte-Marie. A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems -- Analysis, assessments and applications to parameter estimation. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2013, 47 (6), pp.1821-1843. ⟨10.1051/m2an/2013090⟩. ⟨hal-00834397⟩

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