Related papers: Long-time behavior of a finite volume discretizati…
We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced by Bailo, Carrillo, and Hu (2020). Crucially, this scheme keeps the dissipation…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
The Vlasov-Fokker-Planck equation describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that…
We study the asymptotic and pre-asymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient $D_{\mathrm{eff}}$ is numerically determined by the asymptotic…
The algorithm for the DPD fluid, the dynamics of which is conceptually a combination of molecular dynamics, Brownian dynamics and lattice gas automata, is designed for simulating rheological properties of complex fluids on hydrodynamic time…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
We revisit the variational characterization of conservative diffusion as entropic gradient flow and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for…
This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
In this article, two kinds of numerical algorithms are derived for the ultra-slow (or superslow) diffusion equation in one and two space dimensions, where the ultra-slow diffusion is characterized by the Caputo-Hadamard fractional…
Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically…
We propose and analyse a spatial discretization of the non-local Quantum Drift Diffusion (nlQDD) model by Degond, M\`{e}hats and Ringhofer in one space dimension. With our approach, that uses consistently matrices on ${\mathbb C}^N$ instead…
In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function…
The authors present a study of the non equilibrium statistical properties of a one dimensional hard-rod fluid dissipating energy via inelastic collisions and subject to the action of a Gaussian heat bath, simulating an external driving…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
We study whether fine discretization (i.e., terracing) of continuous pair interactions, when used in combination with first-order mean-spherical approximation theory, can lead to a simple and general analytical strategy for predicting the…
This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous…
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…