A variational formulation of the BDF2 method for metric gradient flows

DOI10.1051/m2an/2018045zbMath1416.65150arXiv1711.02935OpenAlexW2962845679MaRDI QIDQ5226424

Simon Plazotta, Daniel Matthes

Publication date: 31 July 2019

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.02935

zbMATH Keywords

gradient flowparabolic equationsnonlinear diffusion equationsminimizing movementssecond order schemeBDF2multistep discretization

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Evolution inclusions (34G25) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Initial value problems for nonlinear higher-order PDEs (35G25) Numerical solutions to abstract evolution equations (65J08) Initial value problems for higher-order parabolic systems (35K46)

Related Items (13)

Primal dual methods for Wasserstein gradient flows ⋮ A new minimizing-movements scheme for curves of maximal slope ⋮ High order schemes for gradient flow with respect to a metric ⋮ Structure-preserving integrators for dissipative systems based on reversible– irreversible splitting ⋮ A BDF2-approach for the non-linear Fokker-Planck equation ⋮ A Variational Lagrangian Scheme for a Phase-Field Model: A Discrete Energetic Variational Approach ⋮ Lagrangian schemes for Wasserstein gradient flows ⋮ A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games ⋮ Particle-based energetic variational inference ⋮ Simulation of multiphase porous media flows with minimising movement and finite volume schemes ⋮ Two structure-preserving time discretizations for gradient flows ⋮ Data-driven gradient flows ⋮ A dynamic mass transport method for Poisson-Nernst-Planck equations

Uses Software

• RODAS

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