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Mathematics > Numerical Analysis

arXiv:1504.05982 (math)
[Submitted on 22 Apr 2015]

Title:A convergent explicit finite difference scheme for a mechanical model for tumor growth

Authors:Konstantina Trivisa, Franziska Weber
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Abstract: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 imaging 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 (Mathematical Topics in Fluid Dynamics, 1998).
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
MSC classes: 35Q30
Cite as: arXiv:1504.05982 [math.NA]
  (or arXiv:1504.05982v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1504.05982

Submission history

From: Franziska Weber [view email]
[v1] Wed, 22 Apr 2015 20:47:25 UTC (84 KB)
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