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

Title data

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

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Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: singular Hamilton-Jacobi equations; maximal solution; regularization; numerical approximation; degenerate Hamilton-Jacobi equations; error bound; viscosity solution; eikonal equation; shape-from-shading problem
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Result of work at the UBT: No
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 22 Feb 2021 09:04
Last Modified: 07 May 2021 07:14
URI: https://eref.uni-bayreuth.de/id/eprint/63267