{
  "abstract": "This paper presents the first $L^2$-norm error analysis for a nonlinear thermoelastic system with acoustic boundary conditions. The model involves three coupled variables: the acoustic potential $u$, the temperature $θ$, and the normal displacement to the boundary $δ$, with nonlinearities $|u|^d u$ in the domain and $g(\\cdot,u')$ on the boundary, in addition to a nonlocal term $β(\\int_Ωθdx)Δθ$ in the heat equation. We establish error estimates for the fully discrete problem, using the Crank-Nicolson method for time discretization and finite element method with basis of degree $r \\geqslant 1$ for space discretization. We demonstrate that the domain-boundary coupling induces a half-power loss in the spatial convergence order for the variable $u$, and this effect propagates to the remaining variables due to the thermoelastic and boundary couplings, resulting in the final error estimate $\\mathcal{O}(h^{r+\\frac{1}{2}} + τ^2)$. A bootstrap argument is employed to ensure the uniform boundedness of $\\|U_h^n\\|_{L^\\infty}$, which is essential for handling the nonlinearity. Numerical results using Lagrange finite element basis of degrees $ r = 1, 2, 3 $ (linear, quadratic, and cubic) corroborate the theoretical estimates and illustrate the transition from suboptimal to optimal convergence orders when the exact solution possesses additional $L^\\infty$ regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24704",
  "author_total": 4,
  "authors": [
    {
      "name": "Adriano A. Alcântara"
    },
    {
      "name": "Bruno A. Carmo"
    },
    {
      "name": "Juan B. Límaco"
    },
    {
      "name": "Carlos M. Guzmán"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dng2hed42b0w5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24704",
  "fulltext_url": null,
  "id": "dng2hed42b0w5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24704",
  "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": "W7223038945",
  "pdf_url": "https://arxiv.org/pdf/2610.24704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dng2hed42b0w5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24704"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Numerical Analysis for a Nonlinear Coupled Thermoelastic System with Acoustic Boundary Conditions",
  "title_text": "Numerical Analysis for a Nonlinear Coupled Thermoelastic System with Acoustic Boundary Conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/dng2hed42b0w5",
  "venue": "arXiv",
  "versions": []
}