Numerical Discretization of Boundary Conditions for First Order Hamilton--Jacobi Equations

Authors:
Rémi Abgrall
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2003

Citing 0
Cited 5

High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes

Journal of Scientific Computing
An Introduction to Eulerian Geometrical Optics (1992–2002)

Journal of Scientific Computing
An anti-diffusive scheme for viability problems

Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
A numerical study for the homogenisation of one-dimensional models describing the motion of dislocations

International Journal of Computing Science and Mathematics
On the Numerical Approximation of First-Order Hamilton-Jacobi Equations

International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

We provide two simple ways of discretizing a large class of boundary conditions for first order Hamilton--Jacobi equations. We show the convergence of the numerical scheme under mild assumptions. However, many types of such boundary conditions can be written in this way. Some provide "good" numerical results (i.e., without boundary layers), whereas others do not. To select a good one, we first give some general results for monotone schemes which mimic the maximum principle of the continuous case, and then we show in particular cases that no boundary layer can exist. Some numerical applications illustrate the method. An extension to a geophysical problem is also considered.