Study of a chemo-repulsion model with quadratic production. I: Analysis of the continuous problem and time-discrete numerical schemes

DOI10.1016/j.camwa.2020.04.009zbMath1447.65076arXiv1803.02386OpenAlexW3030293866MaRDI QIDQ2194790

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/1803.02386

zbMATH Keywords

convergenceerror estimatesenergy-stabilitychemo-repulsion modelquadratic productionfirst-order time schemes

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with biology, chemistry and other natural sciences (35Q92) 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)

Related Items (11)

On a bi-dimensional chemo-repulsion model with nonlinear production and a related optimal control problem ⋮ Linear energy stable numerical schemes for a general chemo-repulsive model ⋮ Finite element analysis of attraction-repulsion chemotaxis system. I: Space convergence ⋮ An Optimal Control Problem Subject to Strong Solutions of Chemotaxis-Consumption Models ⋮ Unconditionally energy-stable discontinuous Galerkin method for the chemo-repulsion-Navier-Stokes system ⋮ Convergence of a Time Discrete Scheme for a Chemotaxis-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

Uses Software

• Chemotaxis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonnegativity of exact and numerical solutions of some chemotactic models
• Fully discrete analysis of a discontinuous finite element method for the keller-segel chemotaxis model
• Functional spaces for the theory of elliptic partial differential equations. Transl. from the French by Reinie Erné
• Characteristic splitting mixed finite element analysis of Keller-Segel chemotaxis models
• Infinite-dimensional dynamical systems in mechanics and physics.
• Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis
• A finite volume scheme for the Patlak-Keller-Segel chemotaxis model
• Conservative upwind finite-element method for a simplified Keller–Segel system modelling chemotaxis
• Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
• 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
• Monotone combined edge finite volume–finite element scheme for Anisotropic Keller–Segel model
• Numerical simulation of chemotactic bacteria aggregation via mixed finite elements
• Singular limits in thermodynamics of viscous fluids

This page was built for publication: Study of a chemo-repulsion model with quadratic production. I: Analysis of the continuous problem and time-discrete numerical schemes