Work

On the Existence and Uniqueness of Numerical Solutions for Heterogeneous Duhem Operators

Year: 2026

Type: article

Abstract: In this work, we propose a multiscale finite element method for solving heterogeneous nonlinear parabolic problems involving Duhem operators that model hysteresis in spatially varying media. A formulation of the method is introduced to facilitate the mathematical analysis, linking microscopic heterogeneities to macroscopic behavior. We establish the existence, uniqueness and boundedness of the numerical solution for both periodic and Dirichlet coupling scenarios, laying a strong foundation for the practical implementation of the multiscale method in computational settings.

Source: Acta Applicandae Mathematicae

DOI: 10.1007/s10440-026-00785-7

Authors: Achille Landri Pokam Kakeu, Mapundi Kondwani Banda

Institution: University of Pretoria

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Research Foundation, University of Pretoria, South African Agency for Science and Technology Advancement