Numerical Simulation of Diffusive and Aggregation Phenomena in Nonlinear Continuity Equations by Evolving Diffeomorphisms
- Carrillo, José Antonio 1234
- Moll, Salvador 5
- 1 CRM - Centre de Recerca Matemàtica
- 2 Institució Catalana de Recerca i Estudis Avançats (ICREA)
- 3 Imperial College, London
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4
Universitat Autònoma de Barcelona
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5
Universitat de València
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ISSN: 1064-8275, 1095-7197
Année de publication: 2010
Volumen: 31
Número: 6
Pages: 4305-4329
Type: Article
D'autres publications dans: SIAM Journal on Scientific Computing
Résumé
We propose a numerical algorithm for solving nonlinear continuity equations written in Lagrangian coordinates. This transformation is intimately related to variational approaches for the well-posedness of gradient flows of energy functionals with respect to the quadratic transportation distance in optimal transport theory. These schemes allow the numerical approximation of both diffusive and aggregation regimes of different models. Positivity, energy decreasing, and mesh adaptation are built-in in the numerical scheme, and thus we are capable of capturing blow-up densities and of dealing with vacuum regions and merging of mass patches in a natural way.
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