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Semi-Lagrangian Schemes for Hamilton–Jacobi Equations, Discrete Representation Formulae and Godunov Methods

✍ Scribed by M. Falcone; R. Ferretti

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 379 KB
Volume: 175
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.2001.6954

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✦ Synopsis

We study a class of semi-Lagrangian schemes which can be interpreted as a discrete version of the Hopf-Lax-Oleinik representation formula for the exact viscosity solution of first order evolutive Hamilton-Jacobi equations. That interpretation shows that the scheme is potentially accurate to any prescribed order. We discuss how the method can be implemented for convex and coercive Hamiltonians with a particular structure and how this method can be coupled with a discrete Legendre trasform. We also show that in one dimension, the first-order semi-Lagrangian scheme coincides with the integration of the Godunov scheme for the corresponding conservation laws. Several test illustrate the main features of semi-Lagrangian schemes for evolutive Hamilton-Jacobi equations.

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