{
  "abstract": "Stokes equations are often difficult to handle in geodynamic modelling because they form a saddle-point system and involve strong variations in viscosity. In this work, we reformulate the Uzawa iteration through finite element variational principles, replacing the standard algebraic residual with a weighted L ² form that yields a robust preconditioned conjugate gradient iteration for the Schur complement system. Residuals are evaluated in weak form, giving an effect similar to that of a mass-matrix preconditioner. We also add a projection step so that the velocity field remains nearly divergence-free. These updates made the solver converge faster and behave more stably than the standard Uzawa method. This reformulation provides a complementary algorithmic perspective on Schur complement preconditioning within the finite element variational framework. The modified approach was tested in several cases, including ABC flow, SolCx, SolKz, mantle convection, block sinking, multisinker, and compressible convection under the Anelastic Liquid Approximation.",
  "abstract_shown": true,
  "affiliations": [
    "Kangwon National University (Chuncheon, Korea, Republic of)"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "name": "Deok-Kyu Jang"
    },
    {
      "name": "Kyeong-Min Lee",
      "orcid": "0009-0003-2583-0772"
    },
    {
      "name": "Cedric Thieulot",
      "orcid": "0000-0001-6636-2862"
    },
    {
      "name": "Whan-Hyuk Choi"
    },
    {
      "affs": [
        0
      ],
      "name": "Byung-Dal So",
      "orcid": "0000-0002-9294-7896"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eqctbf6r726cv.bib",
  "cited_by": 0,
  "doi": "10.5194/se-17-1167-2026",
  "fulltext_url": null,
  "id": "eqctbf6r726cv",
  "issns": [
    "1869-9529"
  ],
  "landing_url": "https://se.copernicus.org/articles/17/1167/2026/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W4416334638",
  "pdf_url": "https://se.copernicus.org/articles/17/1167/2026/se-17-1167-2026.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": "Copernicus GmbH",
  "ris": "https://research.draconitic.com/paper/eqctbf6r726cv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:40Z",
      "native_id": "10.5194/se-17-1167-2026",
      "source": "crossref",
      "url": "https://se.copernicus.org/articles/17/1167/2026/"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "issn:1869-9529",
      "subfield": "geophysics"
    }
  ],
  "title": "Efficient Uzawa algorithms with projection strategies for geodynamic Stokes flow",
  "title_text": "Efficient Uzawa algorithms with projection strategies for geodynamic Stokes flow",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:20:40Z",
  "url": "https://research.draconitic.com/paper/eqctbf6r726cv",
  "venue": "Solid Earth",
  "versions": [
    {
      "doi": "10.5194/egusphere-2025-5480",
      "pid": null,
      "relation": "preprint",
      "title": null,
      "venue": null
    }
  ]
}