From a cell model with active motion to a Hele-Shaw-like system. A numerical approach
Numerical Analysis
2018-05-22 v1
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.
Cite
@article{arxiv.1805.07658,
title = {From a cell model with active motion to a Hele-Shaw-like system. A numerical approach},
author = {Francisco Guillén-González and Juan Vicente Gutiérrez-Santacreu},
journal= {arXiv preprint arXiv:1805.07658},
year = {2018}
}
Comments
23 pages, 5 figures