Numerical Approximation of the Maximal Solutions for a Class of Degenerate Hamilton-Jacobi Equations

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Camilli, Fabio ; Grüne, Lars:
Numerical Approximation of the Maximal Solutions for a Class of Degenerate Hamilton-Jacobi Equations.
In: SIAM Journal Numerical Analysis. Bd. 38 (2000) Heft 5 . - S. 1540-1560.
ISSN 1095-7170
DOI: https://doi.org/10.1137/S003614299834798X

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Abstract

In this paper we study an approximation scheme for a class of Hamilton-Jacobi problems for which uniqueness of the viscosity solution does not hold. This class includes the Eikonal equation arising in the Shape from Shading problem. We show that, if an appropriate stability condition is satisfied, the scheme converges to the maximal viscosity solution of the problem. Furthermore, we give an estimate for the discretization error.