Displaying similar documents to “Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group”

On the numerical approximation of first-order Hamilton-Jacobi equations

Rémi Abgrall, Vincent Perrier (2007)

International Journal of Applied Mathematics and Computer Science

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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.

On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations

Guy Barles, Espen Robstad Jakobsen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov...