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In a short introduction, I will explain what is cross diffusion, physical phenomenons producing these systems, an example of these systems and a few key mathematical challenges and results.
Then I will illustrate the key ideas of the discretization and numerical analysis of the example presented in the introduction in a simplified setting. After that, I intend to provide a brief explanation on how these techniques should be adapted to the full system.
If there is enough time, I would like to give a brief overview on a way to couple distinct possibly non-smooth physical phenomena in a thermodynamically consistant way.