Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Barakat, Mohamed, Guignard, Diane
Institution: University of Ottawa
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G6956711515
OpenAlex ID: W7214894524