Related papers: A particle micro-macro decomposition based numeric…
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the…
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order partial differential equations. By decoupling the primary PDE…
In this work, we investigate a system of interacting particles governed by a set of stochastic differential equations. Our main goal is to rigorously demonstrate that the empirical measure associated with the particle system converges…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…
We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and long time dynamics for the PDE model. The PDE, originally…
We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…
Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of…
In this work we first prove, by formal arguments, that the diffusion limit of nonlinear kinetic equations, where both the transport term and the turning operator are density-dependent, leads to volume-exclusion chemotactic equations. We…
We study the existence and the rate of equilibration of weak solutions to a two-component system of non-linear diffusion-aggregation equations, with small cross diffusion effects. The aggregation term is assumed to be purely attractive, and…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
We present a finite volume scheme for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with size exclusion yielding cross-diffusion. Our method…
Granular materials are characterized by large collections of discrete particles of sizes larger than one micron, where the particle-particle interactions are significantly more important than the particle-fluid interactions. These flows can…
The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
The aim of this paper is to investigate the unstable nature of pressure computation focusing on incompressible flow modeling through the projection-based particle methods. A new approach from the original viewpoint of the momentum…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sciences. The approximating particle system is a nonlocal…