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The 3DVAR filter for the Navier-Stokes equation: Accuracy and stability in the limit of high-frequency observations

The 3DVAR filter for the Navier-Stokes equation: Accuracy and stability in the limit of high-frequency observations
The 3DVAR filter for the Navier-Stokes equation: Accuracy and stability in the limit of high-frequency observations
We study the problem of accuracy and stability of filters for the Navier-Stokes equation in continuous time. In particular, we formally derive continuous filters from discrete filters in the frequent observations limit and focus on the 3DVAR case in which the covariance is assumed to be constant. The diffusion limit of continuous observations gives rise to a Stochastic Partial Differential Equation (SPDE) describing the time evolution of the estimated posterior filtering mean. Accuracy of this filter is established in the mean square sense.
Stochastic Partial Differential Equations, Navier-Stokes, 3DVAR, filtering, continuous-feedback control
978-0-7354-1091-6
916-919
Blömker, D.
8a16a87c-3447-4a10-9378-9d946977d639
Law, K. J. H.
f9315274-c933-45c4-9408-6e6dc0ab9b25
Stuart, A. M.
73a28e88-c221-4f8b-9e76-4115d7896029
Zygalakis, K. C.
0f7587cb-0895-4637-98b3-7f9104cf9ea2
Blömker, D.
8a16a87c-3447-4a10-9378-9d946977d639
Law, K. J. H.
f9315274-c933-45c4-9408-6e6dc0ab9b25
Stuart, A. M.
73a28e88-c221-4f8b-9e76-4115d7896029
Zygalakis, K. C.
0f7587cb-0895-4637-98b3-7f9104cf9ea2

Blömker, D., Law, K. J. H., Stuart, A. M. and Zygalakis, K. C. (2012) The 3DVAR filter for the Navier-Stokes equation: Accuracy and stability in the limit of high-frequency observations. Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics, Greece. 19 - 25 Sep 2012. pp. 916-919 . (doi:10.1063/1.4756291).

Record type: Conference or Workshop Item (Paper)

Abstract

We study the problem of accuracy and stability of filters for the Navier-Stokes equation in continuous time. In particular, we formally derive continuous filters from discrete filters in the frequent observations limit and focus on the 3DVAR case in which the covariance is assumed to be constant. The diffusion limit of continuous observations gives rise to a Stochastic Partial Differential Equation (SPDE) describing the time evolution of the estimated posterior filtering mean. Accuracy of this filter is established in the mean square sense.

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More information

Published date: 2012
Venue - Dates: Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics, Greece, 2012-09-19 - 2012-09-25
Keywords: Stochastic Partial Differential Equations, Navier-Stokes, 3DVAR, filtering, continuous-feedback control
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 355730
URI: https://eprints.soton.ac.uk/id/eprint/355730
ISBN: 978-0-7354-1091-6
PURE UUID: 5b9bb682-5d63-4423-bfd4-31f87310b1c4

Catalogue record

Date deposited: 04 Sep 2013 15:37
Last modified: 18 Jul 2017 03:45

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