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math.NA2026
Discrete Sobolev and Trudinger inequalities on polyhedral meshes
Maxime Herda, Ariane Trescases, Antoine Zurek
We revisit the derivation of discrete Sobolev and related inequalities on bounded domains for piecewise constant functions on polyhedral meshes. Our results improve the dependence…
math.NA2024
A finite volume scheme for the local sensing chemotaxis model
Maxime Herda, Ariane Trescases, Antoine Zurek
In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion system which models chemotaxis with local sensing. This system has the same Lyapunov func…