Data assimilation for the Navier-Stokes equations using local observables
| dc.contributor.author | Biswas, Animikh | |
| dc.contributor.author | Bradshaw, Zachary | |
| dc.contributor.author | Jolly, Michael S. | |
| dc.date.accessioned | 2020-09-11T16:54:42Z | |
| dc.date.available | 2020-09-11T16:54:42Z | |
| dc.date.issued | 2021-10-28 | |
| dc.description.abstract | We develop, analyze, and test an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier--Stokes equations on the torus. We prove that, for any error threshold, if the reference flow is analytic with sufficiently large analyticity radius, then it can be recovered within that threshold. Numerical computations are included to demonstrate the effectiveness of this approach, as well as variants with data on moving subdomains. In particular, we demonstrate numerically that machine precision synchronization is achieved for mobile data collected from a small fraction of the domain. | en_US |
| dc.description.sponsorship | The research of the second author was supported in part by Simons Foundation grant 635438. The research of the third author was supported in part by NSF grant DMS-1818754. This work was supported by the Lilly Endowment, Inc., through its support for the Indiana University Pervasive Technology Institute, which provided supercomputing resources used for this research. | |
| dc.description.uri | https://epubs.siam.org/doi/10.1137/20M136058X | en_US |
| dc.format.extent | 30 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.identifier | doi:10.13016/m2a6xx-zwnr | |
| dc.identifier.citation | Biswas, Animikh, Zachary Bradshaw, and Michael S. Jolly. “Data Assimilation for the Navier--Stokes Equations Using Local Observables.” SIAM Journal on Applied Dynamical Systems 20, no. 4 (January 2021): 2174–2203. https://doi.org/10.1137/20M136058X. | en_US |
| dc.identifier.uri | https://doi.org/10.1137/20M136058X | |
| dc.language.iso | en_US | en_US |
| dc.publisher | SIAM | |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | |
| dc.title | Data assimilation for the Navier-Stokes equations using local observables | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0001-8594-0568 |