Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system

DOI10.5802/smai-jcm.18zbMath1416.65339OpenAlexW2603908629MaRDI QIDQ4967349

Clément Cancès, Moustafa Ibrahim, Mazen Saad

Publication date: 3 July 2019

Published in: The SMAI journal of computational mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/smai-jcm.18

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Computational methods for problems pertaining to biology (92-08) Cell movement (chemotaxis, etc.) (92C17) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items

Convergence of nonlinear numerical approximations for an elliptic linear problem with irregular data, Positivity-preserving finite volume scheme for compressible two-phase flows in anisotropic porous media: the densities are depending on the physical pressures, A nonnegativity preserving scheme for the relaxed Cahn–Hilliard equation with single-well potential and degenerate mobility, Simulating the behaviour of glioblastoma multiforme based on patient MRI during treatments, Numerical analysis for two-phase flow with non-equilibrium capillary pressure in anisotropic porous media, Convergence of a positive nonlinear DDFV scheme for degenerate parabolic equations, A positive cell vertex Godunov scheme for a Beeler–Reuter based model of cardiac electrical activity, Numerical analysis of a three-species chemotaxis model, Linearized implicit methods based on a single-layer neural network: application to Keller-Segel models, Positive nonlinear DDFV scheme for a degenerate parabolic system describing chemotaxis, Positive control volume finite element scheme for a degenerate compressible two-phase flow in anisotropic porous media, Convergence of a positive nonlinear control volume finite element scheme for solving an anisotropic degenerate breast cancer development model, Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations
• Monotone corrections for generic cell-centered finite volume approximations of anisotropic diffusion equations
• Finite volume methods for degenerate chemotaxis model
• On the finite volume element method
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Quasilinear elliptic-parabolic differential equations
• Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
• The gradient discretisation method
• Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
• Convergence of finite volume schemes for a degenerate convection-diffusion equation arising in flows in porous media
• A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs
• 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
• 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
• 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
• Finite volume schemes for diffusion equations: Introduction to and review of modern methods
• Some Discrete Functional Analysis Tools
• Monotone combined edge finite volume–finite element scheme for Anisotropic Keller–Segel model