From a cell model with active motion to a Hele–Shaw-like system: a numerical approach

  • Francisco Guillén-González
  • Juan Vicente Gutiérrez-SantacreuEmail author


In this paper we deal with the numerical solution of a Hele–Shaw-like system via a cell model with active motion. Convergence of approximations is established for well-posed initial data. These data are chosen in such a way that the time derivative is positive at the initial time. The numerical method is constructed by means of a finite element procedure together with the use of a closed-nodal integration. This gives rise to an algorithm which preserves positivity whenever a right-angled triangulation is considered. As a result, uniform-in-time a priori estimates are proved which allows us to pass to limit towards a solution to the Hele–Shaw problem.

Mathematics Subject Classification

92C50 35B25 35K55 35Q92 35R35 76D27 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Francisco Guillén-González
    • 1
  • Juan Vicente Gutiérrez-Santacreu
    • 2
    Email author
  1. 1.Dpto. E.D.A.N. and IMUSUniversidad de SevillaSevillaSpain
  2. 2.Dpto. de Matemática Aplicada I, E. T. S. I. InformáticaUniversidad de SevillaSevillaSpain

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