Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on image analysis. This work deals with the numerical approximation of a mechanical model for tumor growth and the analysis of its dynamics. The system under investigation is given by a multi-phase flow model: The densities of the different cells are governed by a transport equation for the evolution of tumor cells, whereas the velocity field is given by a Brinkman regularization of the classical Darcy’s law. An efficient finite difference scheme is proposed and shown to converge to a weak solution of the system. Our approach relies on convergence and compactness arguments in the spirit of Lions [P.-L. Lions, Mathematical topics in fluid mechanics. Vol. 2. Vol. 10 of Oxford Lecture Series Math. Appl. The Clarendon Press, Oxford University Press, New York (1998)].
Accepté le :
DOI : 10.1051/m2an/2016014
Mots clés : Tumor growth models, cancer progression, mixed models, multi-phase flow, finite difference scheme, existence
@article{M2AN_2017__51_1_35_0,
author = {Trivisa, Konstantina and Weber, Franziska},
title = {A convergent explicit finite difference scheme for a mechanical model for tumor growth},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {35--62},
publisher = {EDP-Sciences},
volume = {51},
number = {1},
year = {2017},
doi = {10.1051/m2an/2016014},
mrnumber = {3601000},
zbl = {1360.35197},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016014/}
}
TY - JOUR AU - Trivisa, Konstantina AU - Weber, Franziska TI - A convergent explicit finite difference scheme for a mechanical model for tumor growth JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 35 EP - 62 VL - 51 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016014/ DO - 10.1051/m2an/2016014 LA - en ID - M2AN_2017__51_1_35_0 ER -
%0 Journal Article %A Trivisa, Konstantina %A Weber, Franziska %T A convergent explicit finite difference scheme for a mechanical model for tumor growth %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 35-62 %V 51 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016014/ %R 10.1051/m2an/2016014 %G en %F M2AN_2017__51_1_35_0
Trivisa, Konstantina; Weber, Franziska. A convergent explicit finite difference scheme for a mechanical model for tumor growth. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 35-62. doi : 10.1051/m2an/2016014. http://www.numdam.org/articles/10.1051/m2an/2016014/
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