Study of a chemo-repulsion model with quadratic production. II: Analysis of an unconditionally energy-stable fully discrete scheme

DOI10.1016/j.camwa.2020.04.010zbMath1447.65075arXiv1803.02391OpenAlexW3030791699MaRDI QIDQ2194783

Diego Armando Rueda-Gómez, Maria Angeles Rodríguez-Bellido, Francisco Guillén-González

Publication date: 7 September 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.02391

zbMATH Keywords

convergenceerror estimatesfinite element methodfully discrete schemeenergy-stabilitychemorepulsion-production model

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Cell movement (chemotaxis, etc.) (92C17) PDEs in connection with statistical mechanics (35Q82)

Related Items (17)

On a bi-dimensional chemo-repulsion model with nonlinear production and a related optimal control problem ⋮ Numerical analysis of a chemotaxis model for tumor invasion ⋮ Linear energy stable numerical schemes for a general chemo-repulsive model ⋮ Finite element analysis of attraction-repulsion chemotaxis system. I: Space convergence ⋮ Error estimates for the finite element method of the chemotaxis-Navier-Stokes equations ⋮ Unconditionally energy-stable discontinuous Galerkin method for the chemo-repulsion-Navier-Stokes system ⋮ Convergence of a Time Discrete Scheme for a Chemotaxis-Consumption Model ⋮ A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\infty$ estimates for taxis gradients ⋮ A linearized decoupled Crank-Nicolson FEM for Keller-Segel chemotactic model with nonlinear secretion ⋮ Energy-stable and boundedness preserving numerical schemes for the Cahn-Hilliard equation with degenerate mobility ⋮ Finite element numerical schemes for a chemo-attraction and consumption model ⋮ Unconditionally energy stable fully discrete schemes for a chemo-repulsion model ⋮ Theoretical and numerical results for a chemorepulsion model with non-constant diffusion coefficients ⋮ Numerical analysis for a chemotaxis-Navier–Stokes system ⋮ A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes ⋮ Comparison of two finite element schemes for a chemo-repulsion system with quadratic production ⋮ On a chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics: theoretical and numerical analysis

Uses Software

• Chemotaxis

Cites Work

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• Global dynamics in a higher-dimensional repulsion chemotaxis model with nonlinear sensitivity
• Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis
• Fully discrete analysis of a discontinuous finite element method for the keller-segel chemotaxis model
• Characteristic splitting mixed finite element analysis of Keller-Segel chemotaxis models
• Inter-species competition and chemorepulsion
• Global existence and boundedness in a chemorepulsion system with superlinear diffusion
• Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis
• Convergence of a positive nonlinear control volume finite element scheme for solving an anisotropic degenerate breast cancer development model
• A finite volume scheme for the Patlak-Keller-Segel chemotaxis model
• A critical blow-up exponent in a chemotaxis system with nonlinear signal production
• Long time stability and convergence for fully discrete nonlinear galerkin methods
• L^p-THEORY FOR VECTOR POTENTIALS AND SOBOLEV'S INEQUALITIES FOR VECTOR FIELDS: APPLICATION TO THE STOKES EQUATIONS WITH PRESSURE BOUNDARY CONDITIONS
• Unconditionally energy stable fully discrete schemes for a chemo-repulsion model
• A finite volume scheme for a Keller-Segel model with additional cross-diffusion
• Monotone combined edge finite volume–finite element scheme for Anisotropic Keller–Segel model
• The Mathematical Theory of Finite Element Methods
• Numerical simulation of chemotactic bacteria aggregation via mixed finite elements

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