相关论文: Stochastic and variational approach to finite diff…

We present a stochastic and variational aspect of the Lax-Friedrichs scheme applied to hyperbolic scalar conservation laws. This is a finite difference version of Fleming's results ('69) that the vanishing viscosity method is characterized…

A stochastic and variational aspect of the Lax-Friedrichs scheme was applied to hyperbolic scalar conservation laws by Soga [arXiv: 1205.2167v1]. The results for the Lax-Friedrichs scheme are extended here to show its time-global stability,…

This paper presents a new narrow-stencil finite difference method for approximating the viscosity solution of second order fully nonlinear elliptic partial differential equations including Hamilton-Jacobi-Bellman equations. The proposed…

The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…

In this paper, we investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite difference scheme for…

We consider the computation of free energy-like quantities for diffusions in high dimension, when resorting to Monte Carlo simulation is necessary. Such stochastic computations typically suffer from high variance, in particular in a low…

This work proposes and studies numerical schemes for initial value problems of Hamilton--Jacobi equations (HJEs) with a graph individual noise on the Wasserstein space on graphs. Numerically solving such equations is particularly…

The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton-Jacobi equations in the space of probability measures. The method involves leveraging differentiability properties of the…

We obtain new quantitative estimates of the vanishing viscosity approximation for time-dependent, degenerate, Hamilton-Jacobi equations that are neither concave nor convex in the gradient and Hessian entries of the form $\partial_t…

We propose an approximation scheme for a class of semilinear parabolic equations that are convex and coercive in their gradients. Such equations arise often in pricing and portfolio management in incomplete markets and, more broadly, are…

Z^2-periodic entropy solutions of hyperbolic scalar conservation laws and Z^2-periodic viscosity solutions of Hamilton-Jacobi equations are not unique in general. However, uniqueness holds for viscous scalar conservation laws and viscous…

In this paper, we introduce a framework for the discretization of a class of constrained Hamilton-Jacobi equations, a system coupling a Hamilton-Jacobi equation with a Lagrange multiplier determined by the constraint. The equation is…

We investigate rates of convergence for two approximation schemes of time-independent and time-dependent Hamilton-Jacobi equ-ations with Kirchoff junction conditions. We analyze the vanishing viscosity limit and monotone finite-difference…

We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument which is based only on the subadditive structure of maximal subsolutions (solutions of the "metric problem"). This permits us to give…

We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…

We study the speed of convergence in $L^\infty$ norm of the vanishing viscosity process for Hamilton-Jacobi equations with uniformly or strictly convex Hamiltonian terms with superquadratic behavior. Our analysis boosts previous findings on…

Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…

We build a simple and general class of finite difference schemes for first order Hamilton-Jacobi (HJ) Partial Differential Equations. These filtered schemes are convergent to the unique viscosity solution of the equation. The schemes are…

This paper is concerned with monotone (time-explicit) finite difference schemes associated with first order Hamilton-Jacobi equations posed on a junction. They extend the schemes recently introduced by Costeseque, Lebacque and Monneau…

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…