Convergence of a positive nonlinear control volume finite element scheme for solving an anisotropic degenerate breast cancer development model
DOI10.1016/j.camwa.2018.04.037zbMath1419.65059OpenAlexW2807507802MaRDI QIDQ2001698
Moustafa Ibrahim, Mazen Saad, Françoise Foucher
Publication date: 11 July 2019
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2018.04.037
finite element schemeGodunov schemeanisotropic heterogeneous tensorbreast cancer modeldegenerate nonlinear modelnonclassical upwind finite volume scheme
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)
Related Items (3)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Monotone corrections for generic cell-centered finite volume approximations of anisotropic diffusion equations
- Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy
- Prediction of traveling front behavior in a lattice-gas cellular automaton model for tumor invasion
- Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
- Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis
- Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
- A finite volume scheme for anisotropic diffusion problems
- Compactness of discrete approximate solutions to parabolic PDEs -- application to a turbulence model
- An ordinary differential equation model for the multistep transformation to cancer
- Mathematical modelling of radiotherapy strategies for early breast cancer
- A mathematical model of breast cancer development, local treatment and recurrence
- Finite volume scheme for highly anisotropic diffusion operators on unstructured meshes
- On the efficacy of a control volume finite element method for the capture of patterns for a volume-filling chemotaxis model
- Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations
- Transport and Anisotropic Diffusion Models for Movement in Oriented Habitats
- GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS
- Entropy-Diminishing CVFE Scheme for Solving Anisotropic Degenerate Diffusion Equations
- Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
- Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes
- Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
- Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes
- Cancer Modelling and Simulation
- Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system
- Finite volume schemes for diffusion equations: Introduction to and review of modern methods
- Analysis of a Positive CVFE Scheme for Simulating Breast Cancer Development, Local Treatment and Recurrence
- Mathematical study of a petroleum-engineering scheme
- Nonlinear modelling of cancer: bridging the gap between cells and tumours
This page was built for publication: Convergence of a positive nonlinear control volume finite element scheme for solving an anisotropic degenerate breast cancer development model
