Data assimilation for linear parabolic equations: minimax projection method

Sergiy Zhuk, J.E. Frank, Isabelle Herlin, Robert Shorten

Research output: Contribution to journalArticleAcademicpeer-review

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
Original languageEnglish
Pages (from-to)A1174-A1196
Number of pages23
JournalSIAM Journal on Scientific Computing
Volume37
Issue number3
DOIs
Publication statusPublished - 2015

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