As a counterpoint to classical stochastic particle methods for diffusion, we develop a
deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic …

In this paper, we summarize some recent advances related to the energetic variational
approach (EnVarA), a general variational framework of building thermodynamically …

Given a large ensemble of interacting particles, driven by nonlocal interactions and localized
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …

We design and compute first-order implicit-in-time variational schemes with high-order
spatial discretization for initial value gradient flows in generalized optimal transport metric …

Combining the classical theory of optimal transport with modern operator splitting
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …

We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a
limit from a class of nonlocal partial differential equations. The nonlocal equations are …

This chapter reviews different numerical methods for specific examples of Wasserstein
gradient flows: we focus on nonlinear Fokker-Planck equations, but also discuss …

We consider a class of time-dependent second order partial differential equations governed
by a decaying entropy. The solution usually corresponds to a density distribution, hence …

As a counterpoint to classical stochastic particle methods for linear diffusion equations, such
as Langevin dynamics for the Fokker-Planck equation, we develop a deterministic particle …

We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-
linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known …