Numerical Simulation of Diffusive and Aggregation Phenomena in Nonlinear Continuity Equations by Evolving Diffeomorphisms

  1. Carrillo, José Antonio 1234
  2. Moll, Salvador 5
  1. 1 CRM - Centre de Recerca Matemàtica
  2. 2 Institució Catalana de Recerca i Estudis Avançats (ICREA)
  3. 3 Imperial College, London
  4. 4 Universitat Autònoma de Barcelona
    info

    Universitat Autònoma de Barcelona

    Barcelona, España

    ROR https://ror.org/052g8jq94

  5. 5 Universitat de València
    info

    Universitat de València

    Valencia, España

    ROR https://ror.org/043nxc105

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Revista:
SIAM Journal on Scientific Computing

ISSN: 1064-8275,  1095-7197

Año de publicación: 2010

Volumen: 31

Número: 6

Páginas: 4305-4329

Tipo: Artículo

DOI: 10.1137/080739574 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: SIAM Journal on Scientific Computing

Resumen

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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