Mathematical analysis and robust numerical methods for ion transport in deformable porous media
The interplay between mechanical deformation, fluid flow, and ionic transport lies at the heart of many processes in biology, geoscience, and engineering—from how nutrients move through soft tissues to how electrolytes behave in porous electrodes.
What Will You Learn?
- New computational methods for simulating such coupled phenomena, focusing on the interaction between poroelastic materials and electrochemical transport.
- Development and analysis of numerical schemes combining the Biot model of poroelasticity with the Poisson–Nernst–Planck equations, which govern ion motion in the presence of electric fields.
- Mixed finite element methods as a flexible and robust framework for approximating complex, multiphysics systems.
- Mathematical analysis ensuring the well-posedness and stability of the problem, both in continuous and discrete settings, using tools from functional analysis and saddle-point theory.
- Computational examples that validate theoretical findings and demonstrate the practical performance of the proposed methods, providing a solid foundation for future simulations in areas like biomedical engineering, geosciences, and energy storage.
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