Data assimilation for linear parabolic equations: minimax projection method - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles SIAM Journal on Scientific Computing Year : 2015

Data assimilation for linear parabolic equations: minimax projection method

Abstract

In this paper we propose a state estimation method for linear parabolic partial differential equations (PDE) that accounts for errors in the model, truncation, and observations. It is based on an extension of the Galerkin projection method. The extended method models projection coefficients, representing the state of the PDE in some basis, by means of a differential-algebraic equation (DAE). The original estimation problem for the PDE is then recast as a state estimation problem for the constructed DAE using a linear continuous minimax filter. We construct a numerical time integrator that preserves the monotonic decay of a nonstationary Lyapunov function along the solution. To conclude, we demonstrate the efficacy of the proposed method by applying it to the tracking of a discharged pollutant slick in a two-dimensional fluid.
Fichier principal
Vignette du fichier
Zhuk-SIAM-2015.pdf (2.34 Mo) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01174081 , version 1 (08-07-2015)

Identifiers

Cite

Sergiy Zhuk, Frank Jason, Isabelle Herlin, Robert Shorten. Data assimilation for linear parabolic equations: minimax projection method. SIAM Journal on Scientific Computing, 2015, 37 (3), pp.A1174-A1196. ⟨10.1137/13094709X⟩. ⟨hal-01174081⟩
112 View
155 Download

Altmetric

Share

Gmail Facebook X LinkedIn More