Error analysis of proper orthogonal decomposition data assimilation schemes with grad–div estabilization for the Navier–Stokes equations
Entity
UAM. Departamento de MatemáticasPublisher
ElsevierDate
2022-02-08Citation
10.1016/j.cam.2022.114246
Journal of Computational and Applied Mathematics 411 (2022): 114246
ISSN
0377-0427 (print)DOI
10.1016/j.cam.2022.114246Editor's Version
https://doi.org/10.1016/j.cam.2022.114246Subjects
Data assimilation; Fully discrete schemes; Mixed finite elements methods; Navie–Stokes equations; Proper orthogonal decomposition; Uniform-in-time error estimates; MatemáticasRights
© 2022 The Author(s)
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier–Stokes equations is carried out. A grad–div stabilization term is added to the formulation of the POD method. Error bounds with constants independent on inverse powers of the viscosity parameter are derived for the POD algorithm. No upper bounds in the nudging parameter of the data assimilation method are required. Numerical experiments show that, for large values of the nudging parameter, the proposed method rapidly converges to the real solution, and greatly improves the overall accuracy of standard POD schemes up to low viscosities over predictive time intervals
Files in this item
Google Scholar:García Archilla, Bosco
-
Novo Martín, Julia
-
Rubino, Samuele
This item appears in the following Collection(s)
Related items
Showing items related by title, author, creator and subject.