A second-order numerical method for aggregation equations

29 Aug 2018, 09:30
45m
LILLIAD Learning Center

LILLIAD Learning Center

Cité Scientifique, Villeneuve d'Ascq

Speaker

Dr Ulrik Skre Fjordholm (University of Oslo)

Description

Inspired by so-called TVD limiter-based second-order schemes for hyperbolic conservation laws, we develop a second-order accurate numerical method for multi-dimensional aggregation equations. The method allows for simulations to be continued after the first blow-up time of the solution. In the case of symmetric, lambda-convex potentials with a possible Lipschitz singularity at the origin we prove that the method converges in the Monge--Kantorovich distance towards the unique gradient flow solution. This is joint work with José A. Carrillo and Susanne Solem.

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