Lagrangian schemes for Wasserstein gradient flows
From MaRDI portal
Publication:2235781
DOI10.1016/bs.hna.2020.10.002zbMath1473.65185arXiv2003.03803OpenAlexW3009364461MaRDI QIDQ2235781
Daniel Matthes, Marie-Therese Wolfram, José Antonio Carrillo
Publication date: 21 October 2021
Full work available at URL: https://arxiv.org/abs/2003.03803
Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods in optimal control (49M99) Fokker-Planck equations (35Q84)
Related Items (7)
Applications of optimal transportation in the natural sciences. Abstracts from the workshop held February 21--27, 2021 (online meeting) ⋮ On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility ⋮ Convergence of a Lagrangian Discretization for Barotropic Fluids and Porous Media Flow ⋮ An Optimal Mass Transport Method for Random Genetic Drift ⋮ Gradient Flows for Coupling Order Parameters and Mechanics ⋮ On the well-posedness via the JKO approach and a study of blow-up of solutions for a multispecies Keller-Segel chemotaxis system with no mass conservation ⋮ Gradient flows for bounded linear evolution equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Computational Optimal Transport: With Applications to Data Science
- Dimensionality of local minimizers of the interaction energy
- Long-time behavior of a fully discrete Lagrangian scheme for a family of fourth order equations
- Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces
- A convergent Lagrangian discretization for a nonlinear fourth-order equation
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- Discretization of functionals involving the Monge-Ampère operator
- Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model
- Fisher information regularization schemes for Wasserstein gradient flows
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation
- The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
- A convexity principle for interacting gases
- On maps with given Jacobians involving the heat equation
- A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes
- Computations of optimal transport distance with Fisher information regularization
- A blob method for diffusion
- A BDF2-approach for the non-linear Fokker-Planck equation
- Mean-field limit for collective behavior models with sharp sensitivity regions
- Optimal critical mass in the two dimensional Keller-Segel model in \(R^2\)
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Long-time asymptotics of kinetic models of granular flows
- A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
- Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure
- On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift
- Structure preserving schemes for the continuum Kuramoto model: phase transitions
- Convergence of a Newton algorithm for semi-discrete optimal transport
- Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations
- A review of the mean field limits for Vlasov equations
- Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
- Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
- Nonlocal interactions by repulsive-attractive potentials: radial ins/stability
- Stability of flows associated to gradient vector fields and convergence of iterated transport maps
- One-dimensional kinetic models of granular flows
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- Optimal Transport with Proximal Splitting
- Characterization of Radially Symmetric Finite Time Blowup in Multidimensional Aggregation Equations
- A Fully Discrete Variational Scheme for Solving Nonlinear Fokker--Planck Equations in Multiple Space Dimensions
- Numerical Simulation of Diffusive and Aggregation Phenomena in Nonlinear Continuity Equations by Evolving Diffeomorphisms
- An augmented Lagrangian approach to Wasserstein gradient flows and applications
- Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations
- Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
- Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak–Keller–Segel Model
- A Family of Nonlinear Fourth Order Equations of Gradient Flow Type
- Polar factorization and monotone rearrangement of vector‐valued functions
- Lubrication approximation with prescribed nonzero contact anggle
- The Variational Formulation of the Fokker--Planck Equation
- 14. Convergence of a fully discrete variational scheme for a thin-film equation
- Lagrangian Discretization of Crowd Motion and Linear Diffusion
- Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits
- A variational formulation of the BDF2 method for metric gradient flows
- Convergent Lagrangian Discretization for Drift-Diffusion with Nonlocal Aggregation
- Lagrangian Numerical Approximations to One‐Dimensional Convolution‐Diffusion Equations
- Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$
- Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation
- Diffusion-based method for producing density-equalizing maps
- Diffeomorphisms and Nonlinear Heat Flows
- Identification of Asymptotic Decay to Self-Similarity for One-Dimensional Filtration Equations
- On the Volume Elements on a Manifold
This page was built for publication: Lagrangian schemes for Wasserstein gradient flows