 A novel localized least-squares collocation method for coupled bulk-surface problemsZhuochao Tang, Zhuojia Fu, Meng Chen and Leevan Ling Applied Mathematics and Computation, 2025, vol. 492, issue C Abstract: In this paper, we present a novel least-squares formulation of the Generalized Finite Difference Method (GFDM) and utilize its high-order schemes to solve the coupled bulk-surface reaction-diffusion equations. The coupled bulk-surface problems are composed of bulk equations and surface equations and coupled via some Robin-type boundary conditions. For differential operators on curved surfaces, we focus on the extrinsic definition that defines the surface operators using projection operator to tangent spaces of the surface. By utilizing localization and FD data points, the coupled model is discretized as a large sparse system using the LS-GFDM with two sets of arbitrarily distributed points. Compared with the original GFDM, the LS-GFDM brings about the advantage that it gains flexibility to use FD data points at locations different from the unknown nodal solution values. Finally, numerical demonstrations and applications of Turing pattern formations verify the effectiveness and robustness of the proposed method. Keywords: Least-squares; Laplace-Beltrami operator; Extrinsic; Bulk-surface equations; Pattern formations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:492:y:2025:i:c:s0096300324007112 DOI: 10.1016/j.amc.2024.129250 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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