{
  "abstract": "We study an elliptic optimal control problem governed by Darcy's equation in heterogeneous porous media, with pointwise box constraints on the control. The objective functional is formulated via a Radon measure, which allows the desired pressure state to be tracked on observation sets of varying dimension, including points, curves, and subdomains, within a single formulation. The state and adjoint equations are discretized by a symmetric interior penalty discontinuous Galerkin method, yielding a locally mass-conservative approximation that is robust across strong permeability discontinuities, while the control is approximated by piecewise constants. The state, adjoint, and control are retained as primary unknowns in a single coupled optimality system and solved monolithically by a primal-dual active set strategy. We establish stability and well-posedness of the discretization and derive a priori $L^2$ error estimates for both variables. The principal difficulty is the reduced regularity of the adjoint state induced by the measure-valued tracking data. The analysis controls the resulting adjoint-control coupling through an intermediate adjoint driven by the continuous optimal state. Numerical experiments confirm the predicted convergence rates for point, curve, and subdomain observations, exhibit mesh-independent primal-dual active set iteration counts, and demonstrate local mass conservation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30707",
  "author_total": 2,
  "authors": [
    {
      "name": "SeongHee Jeong"
    },
    {
      "name": "Sanghyun Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fzxtrjv774wy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30707",
  "fulltext_url": null,
  "id": "1fzxtrjv774wy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30707",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.30707",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fzxtrjv774wy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30707",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30707"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Monolithic Discontinuous Galerkin Framework for Darcy Optimal Control with Radon-Measure Tracking and Pointwise Control Constraints",
  "title_text": "A Monolithic Discontinuous Galerkin Framework for Darcy Optimal Control with Radon-Measure Tracking and Pointwise Control Constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/1fzxtrjv774wy",
  "venue": "arXiv",
  "versions": []
}