asymptotic preserving
Recently Published Documents


TOTAL DOCUMENTS

227
(FIVE YEARS 61)

H-INDEX

27
(FIVE YEARS 2)

Author(s):  
Xinran Ruan ◽  
Noemi David

Mechanical models of tumor growth based on a porous medium approach have been attracting a lot of interest both analytically and numerically. In this paper, we study the stability properties of a finite difference scheme for a model where the density evolves down pressure gradients and the growth rate depends on the pressure and possibly nutrients. Based on the stability results, we prove the scheme to be asymptotic preserving (AP) in the incompressible limit. Numerical simulations are performed in order to investigate the regularity of the pressure. We study the sharpness of the $L^4$-uniform bound of the gradient, the limiting case being a solution whose support contains a bubble which closes-up in finite time generating a singularity, the so-called focusing solution.


2021 ◽  
pp. 110859
Author(s):  
Pierre Anguill ◽  
Patricia Cargo ◽  
Cedric Énaux ◽  
Philippe Hoch ◽  
Emmanuel Labourasse ◽  
...  

Sign in / Sign up

Export Citation Format

Share Document