Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach
DOI10.1137/20M1317931zbMath1457.65046arXiv2008.06903OpenAlexW3118447626MaRDI QIDQ5147985
Chun Liu, Wenbin Chen, Chenghua Duan, Shenggao Zhou, Xing Ye Yue
Publication date: 29 January 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.06903
PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Variational methods applied to PDEs (35A15) Finite difference methods applied to problems in fluid mechanics (76M20) Degenerate parabolic equations (35K65) 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) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Fokker-Planck equations (35Q84)
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Cites Work
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- A nonlocal continuum model for biological aggregation
- High order semi-implicit schemes for time dependent partial differential equations
- An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations
- A free energy satisfying finite difference method for Poisson-Nernst-Planck equations
- On the minimization problem of sub-linear convex functionals
- Numerical study of a particle method for gradient flows
- Global minimizers for free energies of subcritical aggregation equations with degenerate diffusion
- Energetically stable discretizations for charge transport and electrokinetic models
- A non-Maxwellian steady distribution for one-dimensional granular media
- A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials
- A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems
- An energetic variational approach for the Cahn-Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis
- Structure preserving schemes for nonlinear Fokker-Planck equations and applications
- A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Numerical methods for porous medium equation by an energetic variational approach
- A conservative, free energy dissipating, and positivity preserving finite difference scheme for multi-dimensional nonlocal Fokker-Planck equation
- Positivity preserving finite difference methods for Poisson-Nernst-Planck equations with steric interactions: application to slit-shaped nanopore conductance
- Energetic variational approach in complex fluids: maximum dissipation principle
- Energetic variational approaches in modeling vesicle and fluid interactions
- Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
- On an aggregation model with long and short range interactions
- Stationary States and Asymptotic Behavior of Aggregation Models with Nonlinear Local Repulsion
- Explicit flock solutions for Quasi-Morse potentials
- Energetic variational approaches for incompressible fluid systems on an evolving surface
- Particle, kinetic, and hydrodynamic models of swarming
- How an Initially Stationary Interface Begins to Move in Porous Medium Flow
- Reciprocal Relations in Irreversible Processes. II.
- Convergence of gauge method for incompressible flow
- Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
- A Conservative and Entropy Scheme for a Simplified Model of Granular Media
- Projection Method I: Convergence and Numerical Boundary Layers
- A Finite Volume Scheme for Nonlinear Degenerate Parabolic Equations
- Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits
- Convergence Analysis of a Numerical Scheme for the Porous Medium Equation by an Energetic Variational Approach
- Numerical complete solution for random genetic drift by energetic variational approach
- A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
- Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
