Volume 51, Number 5, September-October 2017
|Page(s)||1827 - 1858|
|Published online||24 October 2017|
An Adaptive Parametrized-Background Data-Weak approach to variational data assimilation
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
Received: 5 March 2016
Revised: 29 January 2017
Accepted: 1 February 2017
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 L2 state-estimation error to improve performance. We also present a priori estimates for the L2 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.
Mathematics Subject Classification: 62-07 / 93E24
Key words: Variational data assimilation / parametrized partial differential equations / model order reduction / kernel methods
© EDP Sciences, SMAI 2017
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