An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations

DOI10.1007/s10915-016-0174-0zbMath1354.35158arXiv1601.02547OpenAlexW2237567459MaRDI QIDQ333224

Zhongming Wang, Hai-liang Liu

Publication date: 28 October 2016

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.02547

zbMATH Keywords

entropy dissipationdiscontinuous GalerkinFokker-Planck

Mathematics Subject Classification ID

Problems related to evolution (92D15) Asymptotic behavior of solutions to PDEs (35B40) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Fokker-Planck equations (35Q84)

Related Items (17)

Positivity-preserving third order DG schemes for Poisson-Nernst-Planck equations ⋮ A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems ⋮ Some recent developments in superconvergence of discontinuous Galerkin methods for time-dependent partial differential equations ⋮ A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials ⋮ A simplified primal‐dual weak Galerkin finite element method for Fokker–Planck‐type equations ⋮ Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure ⋮ Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations ⋮ Convergence analysis of structure‐preserving numerical methods for nonlinear Fokker–Planck equations with nonlocal interactions ⋮ Entropy dissipative higher order accurate positivity preserving time-implicit discretizations for nonlinear degenerate parabolic equations ⋮ A structure-preserving discontinuous Galerkin scheme for the Fisher-KPP equation ⋮ On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations ⋮ A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems ⋮ A conservative, free energy dissipating, and positivity preserving finite difference scheme for multi-dimensional nonlocal Fokker-Planck equation ⋮ Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity ⋮ Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach ⋮ Error Estimates for the Iterative Discontinuous Galerkin Method to the Nonlinear Poisson-Boltzmann Equation ⋮ Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations

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