{
  "abstract": "In this paper, we propose and analyze a novel three-field symmetric formulation for optimal control problems governed by linear thermo-poroelasticity. The state variables are the solid displacement $\\boldsymbol{u}$, the fluid pressure $p$, and the temperature $θ$, and both the distributed fluid source $m_p$ and the distributed heat source $m_θ$ serve as control variables. We prove well-posedness of the symmetric differentiated formulation, establish the existence and uniqueness of an optimal control pair $(\\bar{m}_p,\\bar{m}_θ)$, and derive the first-order necessary optimality conditions via a coupled three-field adjoint system. For the fully discrete scheme based on dG(0) time discretization, we employ a variational discretization approach for both controls and derive a priori error estimates of order $\\mathcal{O}(h^s + Δt)$ for the state, adjoint, and control errors. We also present manufactured-solution experiments that validate the fully discrete optimality system and illustrate the storage-degenerate regime covered by our analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24448",
  "author_total": 1,
  "authors": [
    {
      "name": "Jeonghun J. Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21nkdghej2kx2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24448",
  "fulltext_url": null,
  "id": "21nkdghej2kx2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24448",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "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": "W7214025710",
  "pdf_url": "https://arxiv.org/pdf/2609.24448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/21nkdghej2kx2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24448"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Numerical approximation of distributed optimal control problems governed by linear thermo-poroelasticity",
  "title_text": "Numerical approximation of distributed optimal control problems governed by linear thermo-poroelasticity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/21nkdghej2kx2",
  "venue": "arXiv",
  "versions": []
}