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A Tree-Based Localized Reduced Basis Method for Parametrized Parabolic PDEs — arXiv:2609.36141

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.36141
License (as archived): CC0-1.0
Archived: 2026-10-07T18:06:17.816Z
SHA-256 of the archived text: 105a96f886d51f6196cb2d7c75c4609dc22dd363c4b5009a4ae9b49bee1d36cd
Stable URL of this page: https://metraipolis.com/documento/dc_4c39abe400a5

How to cite

A Tree-Based Localized Reduced Basis Method for Parametrized Parabolic PDEs — arXiv:2609.36141 — arXiv (en), https://arxiv.org/abs/2609.36141 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4c39abe400a5 (Metraipolis archive dc_4c39abe400a5, sha256 105a96f886d51f6196cb2d7c75c4609dc22dd363c4b5009a4ae9b49bee1d36cd)

BibTeX

@misc{dc4c39abe400a5,
  title = {A Tree-Based Localized Reduced Basis Method for Parametrized Parabolic PDEs — arXiv:2609.36141},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.36141},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4c39abe400a5; sha256 105a96f886d51f6196cb2d7c75c4609dc22dd363c4b5009a4ae9b49bee1d36cd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.36141. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose a localized reduced basis method for parametrized parabolic partial differential equations based on an adaptive partitioning of the parameter domain using hierarchical binary trees. A POD-Greedy procedure is employed to construct reduced spaces associated with each parameter subdomain. A certified \emph{a posteriori} error estimator is derived from an inf-sup stability analysis and shown to be equivalent to the underlying approximation error. This equivalence, together with suitable regularity assumptions on the parameter-to-solution map, enables a rigorous convergence analysis and is used to derive a strategy for selecting the number of POD modes to retain in each local reduced space. Numerical experiments for a parametrized convection--diffusion problem demonstrate the effectiveness of the proposed approach and confirm the predicted convergence behavior.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-30 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.36141 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T17:39:14.394Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).