Structure-preserving hybrid finite volume schemes for cross-diffusion systems on general meshes

par Annamaria Massimini (CERMICS)

mardi 17 nov. 2026, 14:00 → 15:00 Europe/Paris

GI041 (UTC - GI)

In this talk, I will present a hybrid finite volume method for the numerical approximation of an anisotropic cross-diffusion system on general polygonal and polyhedral meshes. The system is derived from a mesoscopic stochastic process describing diffusion in solids under a size-exclusion constraint. A key feature of this system is its entropy structure, which is exploited to formulate the numerical scheme in terms of discrete entropy variables, thereby preserving this structure at the discrete level.

In particular, the entropy structure allows us to prove the existence of nonnegative discrete solutions satisfying the size-exclusion constraint, as well as the convergence of the scheme under mesh refinement. The scheme also preserves mass. To the best of our knowledge, this is the first work to propose and analyze a structure-preserving hybrid finite volume scheme for anisotropic cross-diffusion systems on general polygonal and polyhedral meshes.

This is joint work with V. Ehrlacher and J. Moatti [hal-05589824].

Building on this approach, ongoing joint work with V. Ehrlacher, A. Harnist, J. Moatti, and A. Zurek focuses on developing a structure-preserving hybrid finite volume scheme on general meshes for the Shigesada--Kawasaki--Teramoto (SKT) cross-diffusion system arising in population dynamics. I will also briefly discuss this ongoing work at the end of the talk.