A Convergent Entropy Diminishing Finite Volume Scheme for a Cross-Diffusion System
From MaRDI portal
Publication:4970513
DOI10.1137/20M1316093zbMath1450.65094arXiv2001.11222OpenAlexW3003241673MaRDI QIDQ4970513
Clément Cancès, Benoît Gaudeul
Publication date: 14 October 2020
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2001.11222
Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Positive solutions to PDEs (35B09) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Initial-boundary value problems for second-order parabolic systems (35K51)
Related Items (9)
Entropy and convergence analysis for two finite volume schemes for a Nernst-Planck-Poisson system with ion volume constraints ⋮ A convergent finite volume scheme for dissipation driven models with volume filling constraint ⋮ Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system ⋮ Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system ⋮ Stationary solutions and large time asymptotics to a cross-diffusion-Cahn-Hilliard system ⋮ Structure Preserving Finite Volume Approximation of Cross-Diffusion Systems Coupled by a Free Interface ⋮ An Energy Stable and Positivity-Preserving Scheme for the Maxwell--Stefan Diffusion System ⋮ Existence of weak solutions to a cross-diffusion Cahn-Hilliard type system ⋮ A Convergent Structure-Preserving Finite-Volume Scheme for the Shigesada--Kawasaki--Teramoto Population System
Cites Work
- Unnamed Item
- Unnamed Item
- TP or not TP, that is the question
- Convergence of a finite volume scheme for a system of interacting species with cross-diffusion
- Bound preserving and energy dissipative schemes for porous medium equation
- Phase segregation dynamics in particle systems with long range interactions. I: Macroscopic limits
- The gradient discretisation method
- Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
- Analysis of a degenerate parabolic cross-diffusion system for ion transport
- Error estimates for the implicit MAC scheme for the compressible Navier-Stokes equations
- Compactness of discrete approximate solutions to parabolic PDEs -- application to a turbulence model
- Convergence of an implicit Euler Galerkin scheme for Poisson-Maxwell-Stefan systems
- Uniqueness of strong solutions and weak-strong stability in a system of cross-diffusion equations
- A second order numerical scheme for the annealing of metal-intermetallic laminate composite: a ternary reaction system
- Comparison of a finite-element and finite-volume scheme for a degenerate cross-diffusion system for ion transport
- An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems
- Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations
- A positivity-preserving, energy stable and convergent numerical scheme for the Cahn-Hilliard equation with a Flory-Huggins-deGennes energy
- Error Estimate for Time-Explicit Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws
- Entropy Methods for Diffusive Partial Differential Equations
- Nonlinear Poisson–Nernst–Planck equations for ion flux through confined geometries
- Entropy Method and Asymptotic Behaviours of Finite Volume Schemes
- ANALYSIS OF A FINITE VOLUME METHOD FOR A CROSS-DIFFUSION MODEL IN POPULATION DYNAMICS
- Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
- An error estimate for a finite volume scheme for a diffusion–convection problem on a triangular mesh
- Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
- H-Convergence and Numerical Schemes for Elliptic Problems
- Reciprocal Relations in Irreversible Processes. II.
- Linearly Decoupled Energy-Stable Numerical Methods for Multicomponent Two-Phase Compressible Flow
- Improved $L^2$ estimate for gradient schemes and super-convergence of the TPFA finite volume scheme
- Cross-diffusion systems with non-zero flux and moving boundary conditions
- Numerical analysis of a finite volume scheme for a seawater intrusion model with cross‐diffusion in an unconfined aquifer
- Control Volume Approximation of Degenerate Two-Phase Porous Flows
- Error estimates for a numerical approximation to the compressible barotropic Navier–Stokes equations
- Convergence of a positive nonlinear control volume finite element scheme for an anisotropic seawater intrusion model with sharp interfaces
- Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller--Segel Equations
- Why Do We Need Voronoi Cells and Delaunay Meshes?
- Finite volume schemes for diffusion equations: Introduction to and review of modern methods
- Nonlinear Cross-Diffusion with Size Exclusion
- Finite‐volume scheme for a degenerate cross‐diffusion model motivated from ion transport
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- The boundedness-by-entropy method for cross-diffusion systems
- The Asymmetric Gradient Discretisation Method
- Finite Volume Approximation of a Degenerate Immiscible Two-Phase Flow Model of Cahn–Hilliard Type
This page was built for publication: A Convergent Entropy Diminishing Finite Volume Scheme for a Cross-Diffusion System
