Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations
In this paper we analyze a finite element method applied to a continuous downscal-ing data assimilation algorithm for the numerical approximation of the two- and three-dimensionalNavier–Stokes equations corresponding to given measurements on a coarse spatial scale. For repre-senting the coarse mesh...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/152692 |
| Acceso en línea: | https://hdl.handle.net/11441/152692 https://doi.org/10.1137/19M1246845 |
| Access Level: | acceso abierto |
| Palabra clave: | Data assimilation Downscaling Navier–Stokes equations Uniform-in-time error estimates Mixed finite elements |
| Sumario: | In this paper we analyze a finite element method applied to a continuous downscal-ing data assimilation algorithm for the numerical approximation of the two- and three-dimensionalNavier–Stokes equations corresponding to given measurements on a coarse spatial scale. For repre-senting the coarse mesh measurements we consider different types of interpolation operators includinga Lagrange interpolant. We obtain uniform-in-time estimates for the error between a finite elementapproximation and the reference solution corresponding to the coarse mesh measurements. We con-sider both the case of a plain Galerkin method and a Galerkin method with grad-div stabilization.For the stabilized method we prove error bounds in which the constants do not depend on inversepowers of the viscosity. Some numerical experiments illustrate the theoretical results. |
|---|