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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005468
URN to cite this document: urn:nbn:de:bvb:703-epub-5468-5

Title data

Camilli, Fabio ; Grüne, Lars:
Numerical Approximation of the Maximal Solutions for a Class of Degenerate Hamilton-Jacobi Equations.
Bayreuth , 2000

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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.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen In:
SIAM Journal Numerical Analysis. Bd. 38 (2000) Heft 5 . - S. 1540-1560
Keywords: singular Hamilton-Jacobi equations; maximal solution; regularization; numerical approximation; degenerate Hamilton-Jacobi equations; error bound; viscosity solution; eikonal equation; shape-from-shading problem
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: 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
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)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5468-5
Date Deposited: 07 May 2021 07:14
Last Modified: 14 May 2021 09:49
URI: https://epub.uni-bayreuth.de/id/eprint/5468

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