{
  "abstract": "Continuous data assimilation improves flow predictions by continually nudging a model toward available observational data. For slightly compressible flow, a recent model addresses the limitations of velocity-only nudging by assimilating both velocity and pressure data and nudging both quantities into the incompressible Navier-Stokes equations [5]; continuous-in-time error estimates and preliminary experiments show that this joint nudging is effective and substantially reduces the model error relative to velocity-only nudging. Motivated by these results, we carry out the numerical analysis of the model and its finite element discretizations. We establish stability and error estimates for the semi-discrete scheme and for the fully discrete, linearized backward Euler scheme. The analysis shows an infinite predictability horizon: the effect of the initial error decays exponentially in time, and the model error is first order in the observation resolution H and of order $μ_1^{-1/2}$ in the pressure nudging parameter $μ_1$. Balancing these two error terms, we choose $μ_1=\\mathcal{O}(H^{-2})$, which yields the optimal convergence rate. Numerical experiments confirm the predicted rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27647",
  "author_total": 2,
  "authors": [
    {
      "name": "Aytekin Çıbık"
    },
    {
      "name": "Rui Fang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d37rmqk4fxpn4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27647",
  "fulltext_url": null,
  "id": "d37rmqk4fxpn4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27647",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7204838563",
  "pdf_url": "https://arxiv.org/pdf/2608.27647",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d37rmqk4fxpn4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27647",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27647"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Numerical analysis of data assimilation for slightly compressible flow",
  "title_text": "Numerical analysis of data assimilation for slightly compressible flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/d37rmqk4fxpn4",
  "venue": "arXiv",
  "versions": []
}