A convergent explicit finite difference scheme for a mechanical model\n for tumor growth

2015/04/22 by Konstantina Trivisa, Trivisa, Konstantina, Franziska Weber +1 · 1 citation
Computer Science · Engineering · Mathematics · #35Q30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Mathematical Biology Tumor Growth #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1504.05982

openalex publication_date 2015/04/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Mechanical models for tumor growth have been used extensively in recent years\nfor the analysis of medical observations and for the prediction of cancer\nevolution based on imaging analysis. This work deals with the numerical\napproximation of a mechanical model for tumor growth and the analysis of its\ndynamics. The system under investigation is given by a multi-phase flow model:\nThe densities of the different cells are governed by a transport equation for\nthe evolution of tumor cells, whereas the velocity field is given by a Brinkman\nregularization of the classical Darcy's law. An efficient finite difference\nscheme is proposed and shown to converge to a weak solution of the system. Our\napproach relies on convergence and compactness arguments in the spirit of Lions\n(Mathematical Topics in Fluid Dynamics, 1998).\n

Cited by

• Existence and long-time behavior of global strong solutions to a nonlinear model of tumor growth

Related

• On the vanishing viscosity approximation of a nonlinear model for tumor\n growth
• Convergence analysis of a numerical scheme for a tumour growth model
• Uniform convergence for the incompressible limit of a tumor growth model
• An asymptotic preserving scheme for a tumor growth model of porous medium type
• A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model