Large Time Behavior of Nonlinear Finite Volume Schemes for Convection-Diffusion Equations

DOI10.1137/19M1299311zbMath1451.65117arXiv1911.04962OpenAlexW2986337940MaRDI QIDQ5123995

Clément Cancès, Maxime Herda, Claire Chainais-Hillairet, Stella Krell

Publication date: 17 September 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.04962

zbMATH Keywords

finite volume methodslong-time behaviorlogarithmic Sobolev inequalitiesconvection-diffusion equationsentropy methodsdrift-diffusion equationsdiscrete functional inequalities

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Functional inequalities, including subadditivity, convexity, etc. (39B62) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Initial-boundary value problems for second-order parabolic systems (35K51) Fokker-Planck equations (35Q84)

Related Items

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, Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches, A structure preserving hybrid finite volume scheme for semiconductor models with magnetic field on general meshes, A monotone numerical flux for quasilinear convection diffusion equation, A Convergent Structure-Preserving Finite-Volume Scheme for the Shigesada--Kawasaki--Teramoto Population System

Uses Software

• FV_HipoDiff

Cites Work

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• On the Chang and Cooper scheme applied to a linear Fokker-Planck equation
• Entropy methods for reaction-diffusion systems
• Discretization methods for one-dimensional Fokker-Planck operators
• The gradient discretisation method
• A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure
• Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
• Structure preserving schemes for nonlinear Fokker-Planck equations and applications
• Numerical analysis of a nonlinear free-energy diminishing discrete duality finite volume scheme for convection diffusion equations
• Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equations
• Exponential decay of a finite volume scheme to the thermal equilibrium for drift-diffusion systems
• A practical difference scheme for Fokker-Planck equations
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• Entropy-dissipative discretization of nonlinear diffusion equations and discrete Beckner inequalities
• An Entropy Satisfying Conservative Method for the Fokker–Planck Equation of the Finitely Extensible Nonlinear Elastic Dumbbell Model
• Lyapunov functionals for boundary-driven nonlinear drift–diffusion equations
• On discrete functional inequalities for some finite volume schemes
• Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
• Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations
• Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation
• A Truly Two-Dimensional Discretization of Drift-Diffusion Equations on Cartesian Grids
• Topologie et équations fonctionnelles
• Large time behaviors of upwind schemes and $B$-schemes for Fokker-Planck equations on $\mathbb {R}$ by jump processes
• Finite volume schemes for diffusion equations: Introduction to and review of modern methods
• Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations
• Aliasing and two-dimensional well-balanced for drift-diffusion equations on square grids
• A finite volume scheme for a Keller-Segel model with additional cross-diffusion
• A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities