Consistency and convergence for a family of finite volume discretizations of the Fokker–Planck operator
DOI10.1051/m2an/2021078zbMath1485.35356arXiv2002.09385OpenAlexW3214853860MaRDI QIDQ5034839
Martin Heida, Markus Kantner, Artur Stephan
Publication date: 21 February 2022
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2002.09385
Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Discrete approximations in optimal control (49M25) Fokker-Planck equations (35Q84) Finite volume methods for boundary value problems involving PDEs (65N08)
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- On gradient structures for Markov chains and the passage to Wasserstein gradient flows
- Geodesic convexity of the relative entropy in reversible Markov chains
- On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework
- On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion
- On microscopic origins of generalized gradient structures
- Gradient flows of the entropy for finite Markov chains
- A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local Dirichlet problems
- Numerical simulation of semiconductor devices
- The finite volume Scharfetter-Gummel method for steady convection diffusion equations
- A third Strang lemma and an Aubin-Nitsche trick for schemes in fully discrete formulation
- Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics
- Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
- Ricci curvature of finite Markov chains via convexity of the entropy
- Effective diffusion in thin structures via generalized gradient systems and EDP-convergence
- Jump processes as generalized gradient flows
- Homogenisation of one-dimensional discrete optimal transport
- Generalized Scharfetter-Gummel schemes for electro-thermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient
- Fokker-Planck equations for a free energy functional or Markov process on a graph
- A practical difference scheme for Fokker-Planck equations
- Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations
- A Square Root Approximation of Transition Rates for a Markov State Model
- A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
- Finite-volume schemes for noncoercive elliptic problems with Neumann boundary conditions
- Coarse-graining via EDP-convergence for linear fast-slow reaction systems
- Finite Difference Schemes on Triangular Cell-Centered Grids with Local Refinement
- Generalizations of the Logarithmic Mean
- A monotone finite element scheme for convection-diffusion equations
- The Variational Formulation of the Fokker--Planck Equation
- Error Estimates on the Approximate Finite Volume Solution of Convection Diffusion Equations with General Boundary Conditions
- Convergences of the squareroot approximation scheme to the Fokker–Planck operator
- An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations
- Finite Volume Methods for Convection-Diffusion Problems
- A gradient system with a wiggly energy and relaxed EDP-convergence
- Large time behaviors of upwind schemes and $B$-schemes for Fokker-Planck equations on $\mathbb {R}$ by jump processes
- Non-equilibrium Thermodynamical Principles for Chemical Reactions with Mass-Action Kinetics
- Theory of the Flow of Electrons and Holes in Germanium and Other Semiconductors
- An algorithm with guaranteed convergence for finding a zero of a function
- RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER
- Large-time behaviour of a family of finite volume schemes for boundary-driven convection–diffusion equations
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