Energy estimate, optimal solution and convergence analysis for interfaced valued schemes of the fluid–solid interaction

Abdul Hafeez, Taj Munir, Dong Liu, Mohamed Abdelghany Elkotb and Refka Ghodhbani

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: This study investigates the mathematical and numerical properties of energy estimate, regularity, and convergence analysis through the finite element method FEM for coupled bi-domain scenarios with two interface conditions. This includes the Dirichlet-Neumann (DN) coupling, which ensures continuity in flow problems, and the heat flux condition, which governs heat transfer between two regions. These results ensure that solutions are well defined, smooth and bounded, with energy behavior properly considered, which supports the reliability of numerical simulations. The results demonstrate that the DN-coupling conserves energy using one-sided finite differences without imposing stability constraints. In contrast, the heat flux condition, discretized with central differences, requires additional stability measures. Numerical simulations validate the theoretical findings, and the results are presented through detailed graphs and tables. This work provides a solid foundation both analysis and numerical point of view for exploring higher-order approximations and extending the model to two- and three-dimensional problems in complex multi-physics systems.

Keywords: Multi-physics systems; Finite element method; Coupling interface conditions; Smoothness; Regularity and energy conservation (search for similar items in EconPapers)
Date: 2026
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925012317
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925012317

DOI: 10.1016/j.chaos.2025.117218

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().