{
  "abstract": "We prove an impossibility result for finite-range locally computable a posteriori error estimators for the conforming finite element discretization of an elliptic interface problem. For a class of interface problems with a checkerboard cross-point and $\\{1,M\\}$-valued coefficients, we construct two problem instances on the same interface-fitted mesh. The two instances share a piecewise-constant load for which the finite element solution and the data oscillation both vanish. The ratio of their exact energy errors grows at least proportionally to $M^{1/4}$. Locality together with efficiency forces identical estimator values for these instances. The product of reliability and efficiency constants is therefore bounded below by a constant multiple of $M^{1/4}$. Consequently, any locally computable error estimator for interface problems, whether of residual, equilibrated, or recovery type, cannot be simultaneously reliable and efficient with contrast-independent constants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27817",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuwen Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qxn6zr3gngmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27817",
  "fulltext_url": null,
  "id": "3qxn6zr3gngmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27817",
  "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": "W7214152364",
  "pdf_url": "https://arxiv.org/pdf/2609.27817",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qxn6zr3gngmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.27817",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27817"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Locally computable error estimators for conforming approximations of interface problems cannot be robust",
  "title_text": "Locally computable error estimators for conforming approximations of interface problems cannot be robust",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/3qxn6zr3gngmj",
  "venue": "arXiv",
  "versions": []
}