Geodesic
An Adaptive Parametrized-Background Data-Weak approach to variational data assimilation
Taddei, Tommaso1  
1 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1827-1858

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We present an Adaptive Parametrized-Background Data-Weak (APBDW) approach to the steady-state variational data assimilation (state estimation) problem for systems modeled by partial differential equations. The variational formulation is based on the Tikhonov regularization of the PBDW formulation [Y. Maday, A.T. Patera, J.D. Penn and M. Yano, Int. J. Numer. Meth. Eng. 102 (2015) 933–965] for pointwise noisy measurements. We propose an adaptive procedure based on a posteriori estimates of the L 2 state-estimation error to improve performance. We also present a priori estimates for the L 2 state-estimation error that motivate the approach and guide the adaptive procedure. We provide numerical experiments for a synthetic acoustic problem to illustrate the different elements of the methodology, and we consider an experimental thermal patch configuration to demonstrate the applicability of our approach to real physical systems.

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Accepté le :
DOI : 10.1051/m2an/2017005
Classification : 62-07, 93E24
Keywords: Variational data assimilation, parametrized partial differential equations, model order reduction, kernel methods

Taddei, Tommaso 1

1 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA. 
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Taddei, Tommaso. An Adaptive Parametrized-Background Data-Weak approach to variational data assimilation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1827-1858. doi: 10.1051/m2an/2017005

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