{
  "abstract": "This paper considers the lowest-order first type Nédélec edge element method (EEM) on Cartesian grids for the three-dimensional time-harmonic Maxwell equations with a large wave number. New polynomial preserving recovery (PPR) operators are proposed for the curl of the edge element solution and for the solution itself, respectively. Under the condition that $κ^3 h^2 C_{\\mathrm{sol}}$ is sufficiently small, second-order superconvergence estimates are proved for both the recovered curl and the recovered solution, where $κ$ is the wave number, $h$ is the mesh size, and $C_{\\mathrm{sol}}$ is a stability constant associated with the Maxwell solution operator. In particular, the analysis shows that the proposed PPR procedures cannot mitigate the well-known pollution effect inherent to the EEM. To reduce the pollution error, we further propose a new continuous interior penalty edge element method (CIP-EEM) that incorporates an additional normal-jump penalty term. It is shown that by appropriately choosing the penalty parameters, the new CIP-EEM can improve the phase error by two orders in $κh$. Numerical experiments are presented to confirm the theoretical superconvergence results and to demonstrate that the CIP-EEM can effectively reduce the pollution error in the high-frequency regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11064",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuaishuai Lu"
    },
    {
      "name": "Haijun Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pnexd099tvyj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11064",
  "fulltext_url": null,
  "id": "8pnexd099tvyj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11064",
  "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/2609.11064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pnexd099tvyj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Polynomial preserving recoveries of edge element method on Cartesian grids for the time-harmonic Maxwell equations with large wave number",
  "title_text": "Polynomial preserving recoveries of edge element method on Cartesian grids for the time-harmonic Maxwell equations with large wave number",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/8pnexd099tvyj",
  "venue": "arXiv",
  "versions": []
}