{
  "abstract": "We derive an explicit series representation for the Dirichlet problem for Poisson’s equation in a right-isosceles triangle. Linearity is used to decompose the boundary data into three harmonic subproblems, each carrying the prescribed values on a single side, and a fourth Poisson subproblem with homogeneous Dirichlet conditions. The two leg-driven harmonic fields admit simple sine-hyperbolic expansions in the original coordinates, while the hypotenuse-driven field is obtained after a 45∘ rotation and scaling that maps the domain to a symmetric triangle. The remaining forced problem is treated by an eigenfunction expansion of the Dirichlet Laplacian, with coefficients obtained by orthogonal projection. The resulting formula provides a convenient analytic benchmark for assessing numerical solvers on polygonal domains.",
  "abstract_shown": true,
  "affiliations": [
    "Departamento de Engenharia Mecânica, Faculdade de Tecnologia, Universidade de Brasília"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Juliana Zago Dias Feijó"
    },
    {
      "affs": [
        0
      ],
      "name": "Vinícius Coutinho da Silva"
    },
    {
      "affs": [
        0
      ],
      "name": "André von Borries Lopes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cz3smtvfh9t57.bib",
  "cited_by": 0,
  "doi": "10.1186/s13661-026-02344-3",
  "fulltext_url": "https://doi.org/10.1186/s13661-026-02344-3",
  "id": "cz3smtvfh9t57",
  "issns": [
    "1687-2770",
    "1687-2762"
  ],
  "landing_url": "https://doi.org/10.1186/s13661-026-02344-3",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA299.6-433"
    ],
    [
      "openalex",
      "2604|Differential Equations and Boundary Problems"
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  "openalex": "W7223011463",
  "pdf_url": "https://link.springer.com/content/pdf/10.1186/s13661-026-02344-3.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": "SpringerOpen",
  "ris": "https://research.draconitic.com/paper/cz3smtvfh9t57.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:46:10Z",
      "native_id": "5bfa3c1b82a941ac8f4d1e1b876940ef",
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      "url": "https://doi.org/10.1186/s13661-026-02344-3"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Differential Equations and Boundary Problems",
      "subfield": "general"
    }
  ],
  "title": "The Dirichlet problem for Poisson’s equation in a right-isosceles triangle",
  "title_text": "The Dirichlet problem for Poisson’s equation in a right-isosceles triangle",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:46:10Z",
  "url": "https://research.draconitic.com/paper/cz3smtvfh9t57",
  "venue": "Boundary Value Problems",
  "versions": []
}