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arXiv · 1805.07658

From a cell model with active motion to a Hele-Shaw-like system. A numerical approach

Francisco Guillén-González·Juan Vicente Gutiérrez-Santacreu
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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 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 proven which allows us to pass to limit towards a solution to the Hele--Shaw problem.

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Francisco Guillén-González, Juan Vicente Gutiérrez-Santacreu. 2018-05-19. From a cell model with active motion to a Hele-Shaw-like system. A numerical approach. https://arxiv.org/abs/1805.07658

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