{
  "abstract": "We propose and analyse a fully discrete finite element approximation of the three-dimensional incompressible rotating MHD-Boussinesq system with nonlinear power-law ($p$-Laplace) viscosity. Conforming elements are used for the velocity and temperature, $\\mathbf H(\\operatorname{curl})$-conforming Nédélec elements for the magnetic induction, and a semi-implicit backward Euler scheme in time. The discretisation preserves the principal energy structure: the Lorentz and induction terms cancel exactly, while the Coriolis force remains energy neutral. This yields well-posedness and mesh-independent energy stability. The nonlinear power-law diffusion creates two main analytical difficulties. Since a uniform time-derivative estimate for the discrete velocity is unavailable, strong compactness is obtained through a time-translate argument and Simon's compactness criterion. The weak limit of the nonlinear diffusion is then identified by a Minty argument based on a discrete energy $\\limsup$ inequality. Compactness and passage to the limit hold throughout the shear-thickening regime, while identification of a genuine weak solution is obtained in the Newtonian case and, in three dimensions, above an explicit threshold dictated by the Lorentz force rather than by convection. We further establish a priori error estimates without any mesh-time coupling condition. Three-dimensional numerical experiments confirm the stability and convergence behaviour predicted by the analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31091",
  "author_total": 2,
  "authors": [
    {
      "name": "Akash Ashirbad Panda"
    },
    {
      "name": "Evana Islam Sarkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5y67we7j79qw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31091",
  "fulltext_url": null,
  "id": "b5y67we7j79qw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31091",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7223277664",
  "pdf_url": "https://arxiv.org/pdf/2610.31091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5y67we7j79qw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31091"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Finite Element Approximation of Rotating MHD-Boussinesq Flows with Nonlinear Power-Law Viscosity",
  "title_text": "Finite Element Approximation of Rotating MHD-Boussinesq Flows with Nonlinear Power-Law Viscosity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/b5y67we7j79qw",
  "venue": "arXiv",
  "versions": []
}