{
  "abstract": "In this paper, we study finite element approximations of a fourth-order perturbed semilinear partial differential equation that arises naturally in the computation of viscosity solutions to the fully nonlinear Monge--Ampère equation. We develop a novel recovery-based $C^0$ linear finite element method for discretizing this model problem. The key analytical tool is a Miranda--Talenti-type estimate for the recovery operator, which guides the formulation of the discrete scheme and guarantees its well-posedness. We rigorously establish convergence in the $H^2$ norm by employing a fixed-point argument. Furthermore, optimal $H^1$-error estimates are derived using a duality argument. Numerical experiments confirm the efficiency of the proposed method and validate the theoretical convergence results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29536",
  "author_total": 3,
  "authors": [
    {
      "name": "Tianyang Chu"
    },
    {
      "name": "Hailong Guo"
    },
    {
      "name": "Zhimin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bea5vej9f1ssz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29536",
  "fulltext_url": null,
  "id": "bea5vej9f1ssz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29536",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7223213432",
  "pdf_url": "https://arxiv.org/pdf/2610.29536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bea5vej9f1ssz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29536"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A recovery based linear finite element method for the Monge--Ampère equation",
  "title_text": "A recovery based linear finite element method for the Monge--Ampère equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/bea5vej9f1ssz",
  "venue": "arXiv",
  "versions": []
}