{
  "abstract": "We apply Anderson acceleration to the improved Arrow--Hurwicz (IAH) method for the finite element solution of the steady-state incompressible Navier--Stokes equations. The IAH scheme avoids saddle-point solves by decoupling the velocity and pressure updates, but can require prohibitively many iterations, particularly at high Reynolds numbers. To place the acceleration on a rigorous footing, we reformulate the IAH iteration as a nonlinear fixed-point operator $G$ for the grad-div augmented discrete formulation induced by the scheme and establish its well-definedness, Lipschitz continuity, and Fréchet differentiability, thereby verifying the required smoothness conditions locally near the fixed point. Numerical experiments on problems with known analytical solutions, lid-driven cavity flow up to $Re = 15{,}000$, and channel flow over a full step demonstrate that the resulting Anderson-accelerated improved Arrow--Hurwicz algorithm substantially reduces iteration counts and CPU time while retaining the reported manufactured-solution convergence rates and centerline-velocity agreement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01288",
  "author_total": 3,
  "authors": [
    {
      "name": "Sinan Ergen"
    },
    {
      "name": "Mustafa Ağgül"
    },
    {
      "name": "Mustafa Türkyılmazoğlu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8vg1m8x8yy0cd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01288",
  "fulltext_url": null,
  "id": "8vg1m8x8yy0cd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01288",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7206190472",
  "pdf_url": "https://arxiv.org/pdf/2609.01288",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8vg1m8x8yy0cd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01288",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01288"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Accelerating the Improved Arrow--Hurwicz Iteration via the Anderson Algorithm for Steady-State Navier--Stokes Equations",
  "title_text": "Accelerating the Improved Arrow--Hurwicz Iteration via the Anderson Algorithm for Steady-State Navier--Stokes Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/8vg1m8x8yy0cd",
  "venue": "arXiv",
  "versions": []
}