From a cell model with active motion to a Hele–Shaw-like system: a numerical approach
- 5 Downloads
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 Classification92C50 35B25 35K55 35Q92 35R35 76D27
- 4.Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, 3 edn. Texts in Applied Mathematics, 15. Springer, New York (2008)Google Scholar