Error analysis of proper orthogonal decomposition data assimilation schemes with grad–div stabilization for the Navier–Stokes equations
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 paramete...
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| Published in | Journal of computational and applied mathematics Vol. 411; p. 114246 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.09.2022
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| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 1879-1778 |
| DOI | 10.1016/j.cam.2022.114246 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 114246 |
| Author | Novo, Julia García-Archilla, Bosco Rubino, Samuele |
| Author_xml | – sequence: 1 givenname: Bosco surname: García-Archilla fullname: García-Archilla, Bosco email: bosco@esi.us.es organization: Departamento de Matemática Aplicada II, Universidad de Sevilla, Spain – sequence: 2 givenname: Julia surname: Novo fullname: Novo, Julia email: julia.novo@uam.es organization: Departamento de Matemáticas, Universidad Autónoma de Madrid, Spain – sequence: 3 givenname: Samuele orcidid: 0000-0002-4571-1936 surname: Rubino fullname: Rubino, Samuele email: samuele@us.es organization: Department EDAN &IMUS, Universidad de Sevilla, Spain |
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| Keywords | 65M15 76B75 Proper orthogonal decomposition Fully discrete schemes 35Q30 Uniform-in-time error estimates Navie–Stokes equations 65M70 65M60 65M12 Mixed finite elements methods 65M20 Data assimilation |
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| SubjectTerms | Data assimilation Fully discrete schemes Mixed finite elements methods Navie–Stokes equations Proper orthogonal decomposition Uniform-in-time error estimates |
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| Title | Error analysis of proper orthogonal decomposition data assimilation schemes with grad–div stabilization for the Navier–Stokes equations |
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