{
  "abstract": "We study finite element approximations for an optimal control problem with pointwise tracking governed by a semilinear elliptic PDE. The control variable enters the state equation as a reaction coefficient, resulting in a bilinear control, and the cost functional includes point evaluations of the state variable. We propose two discretization schemes: a semidiscrete scheme, where the control variable is not discretized, and a fully discrete scheme, where the control variable is discretized using piecewise constant functions. In two and three dimensions, for both schemes, we establish convergence of discrete solutions and prove a priori error bounds that behave as $\\mathcal{O}(h|\\log h|)$ in the $L^2(Ω)$-norm for approximating a locally optimal control. In two dimensions, these bounds are improved to $\\mathcal{O}(h)$ for the fully discrete scheme and $\\mathcal{O}(h^{2}|\\log h|^2)$ for the semidiscrete scheme. We conclude with numerical experiments that demonstrate the performance of the proposed schemes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31987",
  "author_total": 3,
  "authors": [
    {
      "name": "Enrique Otarola"
    },
    {
      "name": "Daniel Quero"
    },
    {
      "name": "Matias Sasso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkgepn1xwa3w8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31987",
  "fulltext_url": null,
  "id": "fkgepn1xwa3w8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31987",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7214714787",
  "pdf_url": "https://arxiv.org/pdf/2609.31987",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkgepn1xwa3w8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31987",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31987"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Finite element error estimates for a bilinear optimal control problem with pointwise tracking governed by a semilinear elliptic PDE",
  "title_text": "Finite element error estimates for a bilinear optimal control problem with pointwise tracking governed by a semilinear elliptic PDE",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/fkgepn1xwa3w8",
  "venue": "arXiv",
  "versions": []
}