{
  "abstract": "We propose and analyse a fully mixed finite element method for a two-way coupled mechanochemical model of calcium signalling in viscoelastic tissue. The mechanical response follows a Kelvin--Voigt law, with the elastic and viscous stresses, velocity, and spin tensor as unknowns, and the symmetry of the total stress imposed weakly. The reaction-diffusion system for calcium and inactivated inositol triphosphate is also formulated in mixed form, introducing the diffusive flux as an additional unknown. The coupling is bidirectional: calcium generates an active stress, while local dilation feeds back into the calcium dynamics. We establish global existence and uniqueness by reducing the coupled system to an integro-differential problem and subsequently recovering the mixed variables. The semidiscrete scheme is formulated for general conforming finite element spaces and shown to be well posed under a single inf-sup condition. An interpolation operator that commutes with the divergence and preserves the weak symmetry pairing yields optimal a priori error estimates. We specialise the analysis to three families of weakly symmetric finite elements, deriving explicit convergence rates and, for one family, a superconvergent local post-processing of the displacement. Numerical tests in two and three dimensions confirm the predicted convergence rates and illustrate the method through viscoelastic benchmarks and mechanically driven calcium wavetrains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03317",
  "author_total": 3,
  "authors": [
    {
      "name": "Alonso J. Bustos"
    },
    {
      "name": "Jeonghun J. Lee"
    },
    {
      "name": "Ricardo Ruiz-Baier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86fkcmt0zef52.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03317",
  "fulltext_url": null,
  "id": "86fkcmt0zef52",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03317",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.03317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/86fkcmt0zef52.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Fully mixed finite element methods for the coupling of viscoelasticity and reaction-diffusion models",
  "title_text": "Fully mixed finite element methods for the coupling of viscoelasticity and reaction-diffusion models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/86fkcmt0zef52",
  "venue": "arXiv",
  "versions": []
}