On the Existence and Uniqueness of Numerical Solutions for Heterogeneous Duhem Operators
Abstract
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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Piezoelectric Actuators and Control
Composite Material Mechanics
Publication details
- Journal / source
- Acta Applicandae Mathematicae
- Publisher
- Springer Science and Business Media LLC
- Volume
- 202
- Issue
- 1
- Publication date
- 1 April 2026
- Language
- EN