A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model
DOI10.1007/s10444-024-10212-wMaRDI QIDQ6660077
Publication date: 10 January 2025
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Weak solutions to PDEs (35D30) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Cell movement (chemotaxis, etc.) (92C17) Second-order parabolic systems (35K40) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Finite volume methods for boundary value problems involving PDEs (65N08)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Generalizing the Keller-Segel model: Lyapunov functionals, steady state analysis, and blow-up results for multi-species chemotaxis models in the presence of attraction and repulsion between competitive interacting species
- Free energy and self-interacting particles
- Mathematical aspects of discontinuous Galerkin methods.
- Error control for the approximation of Allen-Cahn and Cahn-Hilliard equations with a logarithmic potential
- Precise computations of chemotactic collapse using moving mesh methods
- An optimal Poincaré inequality for convex domains
- Initiation of slime mold aggregation viewed as an instability
- A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
- A user's guide to PDE models for chemotaxis
- From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
- On the constants in \(hp\)-finite element trace inverse inequalities.
- A note on the Poincaré inequality for convex domains
- Mathematical biology. Vol. 1: An introduction.
- Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains
- Local discontinuous Galerkin method for the Keller-Segel chemotaxis model
- From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II
- A positivity-preserving finite element method for chemotaxis problems in 3D
- Energy dissipative local discontinuous Galerkin methods for Keller-Segel chemotaxis model
- Third order positivity-preserving direct discontinuous Galerkin method with interface correction for chemotaxis Keller-Segel equations
- Adaptive moving mesh upwind scheme for the two-species chemotaxis model
- A positivity preserving moving mesh finite element method for the Keller-Segel chemotaxis model
- A finite volume scheme for the Patlak-Keller-Segel chemotaxis model
- Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems
- On the Discrete Poincaré–Friedrichs Inequalities for Nonconforming Approximations of the Sobolev Space H 1
- An optimal control approach to a posteriori error estimation in finite element methods
- Conservative upwind finite-element method for a simplified Keller–Segel system modelling chemotaxis
- Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis
- Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
- Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
- A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
- Design and convergence analysis for an adaptive discretization of the heat equation
- Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions
- Multi-components chemotactic system in the absence of conflicts
- A Numerical Verification Method for a System of FitzHugh-Nagumo Type
- New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model
- Space and time reconstructions in a posteriori analysis of evolution problems
- Introduction
- Fractional step methods applied to a chemotaxis model
- A posteriori error estimates for wave maps into spheres
This page was built for publication: A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model
