Related papers: Approximation of viscous transport and conservativ…
In the present article, we study the numerical approximation of a system of Hamilton-Jacobi and transport equations arising in geometrical optics. We consider a semi-Lagrangian scheme. We prove the well posedness of the discrete problem and…
We study first- and second-order linear transport equations, as well as ODE and SDE flows, with velocity fields satisfying a one-sided Lipschitz condition. Depending on the time direction, the flows are either compressive or expansive. In…
Most numerical schemes proposed for solving BGK models for rarefied gas dynamics are based on the discrete velocity approximation. Since such approach uses fixed velocity grids, one must secure a sufficiently large domain with fine velocity…
An analysis of the error of the upwind scheme for transport equation with discontinuous coefficients is provided. We consider here a velocity field that is bounded and one-sided Lipschitz continuous. In this framework, solutions are defined…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
We study the numerical approximation of time-dependent, possibly degenerate, second-order Hamilton-Jacobi-Bellman equations in bounded domains with nonhomogeneous Dirichlet boundary conditions. It is well known that convergence towards the…
We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman equations on networks. The scheme is explicit and stable under some technical conditions. We prove a convergence theorem and some error…
Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather…
We investigate transport equations associated to a Lipschitz field on some subspace of $\mathbb{R}^N$ endowedwith a general measure $\mu$ in $L^{p}$-spaces $1 < p <\infty$, extending the results obtained in two previous contributions of the…
We develop a mesh-based semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions recast as a non-linear transport problem for a momentum 1-form. A linearly implicit fully…
Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein space. In particular, we consider the Cauchy problem for a transport equation, where the velocity field depends on the measure itself. We deal with…
We consider the traffic control problem of dynamic routing over parallel servers, which arises in a variety of engineering systems such as transportation and data transmission. We propose a semi-gradient, on-policy algorithm that learns an…
We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations…
Semi-Lagrangian (SL) schemes are highly efficient for simulating transport equations and are widely used across various applications. Despite their success, designing genuinely multi-dimensional and conservative SL schemes remains a…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required…
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…
In this paper, we propose a new method for ensuring formally that a controlled trajectory stay inside a given safety set S for a given duration T. Using a finite gridding X of S, we first synthesize, for a subset of initial nodes x of X ,…
In this paper we study an approximation scheme for an Hamilton-Jacobi equation of Eikonal type defined on a network. We introduce an appropriate notion of viscosity solution for this class of equations (see \cite{sc}) and we prove that an…
This paper focusses on the barely understood gap between the weakly nonlinear regime of structure formation and the onset of the virialized regime. While the former is accessed through perturbative calculations and the latter through…