{
  "abstract": "We consider a class of sixth-order elliptic partial differential equations in two and three dimensions subject to simply supported and Cahn--Hilliard-type boundary conditions. Based on the Ciarlet--Raviart reformulation, we recast the sixth-order problem as an equivalent mixed system involving second- and fourth-order equations and establish its well-posedness under suitable assumptions. For the resulting mixed formulation, we propose and analyse two discretization frameworks: a fully non-conforming hybrid high-order (HHO) method on general polytopal meshes and a $C^0$-conforming HHO--finite element method on simplicial meshes. We prove stability and derive optimal-order a priori error estimates for the primary variables under appropriate regularity assumptions. For the fully non-conforming HHO method, we further derive a reliable residual-based a posteriori error estimator. Numerical experiments confirm the theoretical convergence rates and illustrate the robustness of the proposed methods for a range of mobility parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11167",
  "author_total": 3,
  "authors": [
    {
      "name": "Arbaz Khan"
    },
    {
      "name": "Ajay Kumar"
    },
    {
      "name": "Harpal Singh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ppepct9ay5ec.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11167",
  "fulltext_url": null,
  "id": "6ppepct9ay5ec",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11167",
  "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": "W7212304045",
  "pdf_url": "https://arxiv.org/pdf/2609.11167",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ppepct9ay5ec.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11167",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11167"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Mixed Hybrid High-Order Methods for Sixth-Order Problems: Fully Non-conforming and $C^0$-Conforming Discretizations",
  "title_text": "Mixed Hybrid High-Order Methods for Sixth-Order Problems: Fully Non-conforming and C^0-Conforming Discretizations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/6ppepct9ay5ec",
  "venue": "arXiv",
  "versions": []
}