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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月10日

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  • Achille Landri Pokam Kakeu,
  • Mapundi Kondwani Banda

摘要

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.