Geodesic
A convergent explicit finite difference scheme for a mechanical model for tumor growth
Trivisa, Konstantina1  ; Weber, Franziska2
1 Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA.
2 Seminar for Applied Mathematics (SAM), Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 35-62

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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)].

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016014
Classification : 35Q30, 76N10, 46E35
Keywords: Tumor growth models, cancer progression, mixed models, multi-phase flow, finite difference scheme, existence

Trivisa, Konstantina 1 ; Weber, Franziska 2

1 Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA.
2 Seminar for Applied Mathematics (SAM), Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland. 
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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

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