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Analysis of institutional authors

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April 4, 2022
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Error analysis of proper orthogonal decomposition data assimilation schemes with grad–div stabilization for the Navier–Stokes equations

Publicated to:JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 411 114246- - 2022-09-01 411(), DOI: 10.1016/j.cam.2022.114246

Authors: García-Archilla B; Novo J; Rubino S

Affiliations

Univ Autonoma Madrid, Dept Matemat, Madrid, Spain - Author
Univ Seville, Dept EDAN &IMUS, Seville, Spain - Author
Univ Seville, Dept Matemat Aplicada 2, Seville, Spain - Author
Universidad Autónoma de Madrid - Author
Universidad de Sevilla - Author
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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.

Keywords

approximationflowfully discrete schemesmixed finite elements methodsnavie-stokes equationspodproper orthogonal decompositionsimulationstabilityuniformuniform-in-time error estimatesData assimilationFinite-element-methodFully discrete schemesMixed finite elements methodsNavie–stokes equationsProper orthogonal decompositionUniform-in-time error estimates

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2022, it was in position 45/267, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 2.96. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 1.84 (source consulted: FECYT Feb 2024)
  • Field Citation Ratio (FCR) from Dimensions: 5.67 (source consulted: Dimensions Aug 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-08-02, the following number of citations:

  • WoS: 5
  • Scopus: 7

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-08-02:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://repositorio.uam.es/handle/10486/702978

Leadership analysis of institutional authors

the author responsible for correspondence tasks has been NOVO MARTIN, JULIA.