Spectral Viscosity Approximations to Hamilton--Jacobi Solutions

Authors:
Olga Lepsky
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 2

The use of a Legendre pseudospectral viscosity technique to solve a class of nonlinear dynamic Hamilton-Jacobi equations

Computers & Mathematics with Applications
The Chebyshev spectral viscosity method for the time dependent Eikonal equation

Mathematical and Computer Modelling: An International Journal

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Abstract

The spectral viscosity approximate solution of convex Hamilton--Jacobi equations with periodic boundary conditions is studied. It is proved in this paper that the approximation and its gradient remain uniformly bounded, formally spectral accurate, and converge to the unique viscosity solution. The L1-convergence rate of the order $1-\varepsilon \forall \varepsilon 0$ is obtained.