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

Abstract

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 the time derivate is positive at the initial time. The numerical method is constructed by means of a nite 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 proven which allows us to pass to limit towards a solution to the Hele{Shaw problem.