• Medientyp: E-Artikel
  • Titel: Well-posedness and finite element approximation of mixed dimensional partial differential equations
  • Beteiligte: Hellman, Fredrik; Målqvist, Axel; Mosquera, Malin
  • Erschienen: Springer Science and Business Media LLC, 2024
  • Erschienen in: BIT Numerical Mathematics, 64 (2024) 1
  • Sprache: Englisch
  • DOI: 10.1007/s10543-023-01001-w
  • ISSN: 0006-3835; 1572-9125
  • Schlagwörter: Applied Mathematics ; Computational Mathematics ; Computer Networks and Communications ; Software
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  • Beschreibung: AbstractIn this article, a mixed dimensional elliptic partial differential equation is considered, posed in a bulk domain with a large number of embedded interfaces. In particular, well-posedness of the problem and regularity of the solution are studied. A fitted finite element approximation is also proposed and an a priori error bound is proved. For the solution of the arising linear system, an iterative method based on subspace decomposition is proposed and analyzed. Finally, numerical experiments are presented and rapid convergence using the proposed preconditioner is achieved, confirming the theoretical findings.