On the Numerical Approximation of First-Order Hamilton-Jacobi Equations

Authors:
RéMi Abgrall;Vincent Perrier
Affiliations:
Institut de Mathématiques de Bordeaux and INRIA project Scalapplix, Université Bordeaux I, 341 Cours de la Libération, 33 405 Talence;Department of Applied Mathematics, Université Bordeaux I, 341 Cours de la Libération, 33 405 Talence Cedex, France
Venue:
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
Year:
2007

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Abstract

Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.