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Construction of simple, stable and convergent high order schemes for steady first order Hamilton Jacobi equations.

Remi Abgrall 1, 2
1 SCALAPPLIX - Algorithms and high performance computing for grand challenge applications
INRIA Futurs, Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : We develop a very simple algorithm that permits to construct compact, high order schemes for steady first order Hamilton Jacobi equations. The algorithm relies on the blending of a first order scheme and a compact high order one. The blending is conducted in such a way that the scheme is formally high order accurate. A convergence proof is given. We provide several numerical illustrations that demonstrate the effective accuracy of the scheme. The numerical examples use triangular unstructured meshes, but our method may be applied to other kind of meshes. Several implementation remarks are also given.
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https://hal.inria.fr/inria-00114888
Contributor : Rapport de Recherche Inria <>
Submitted on : Thursday, December 7, 2006 - 11:48:50 AM
Last modification on : Thursday, February 11, 2021 - 2:46:02 PM
Long-term archiving on: : Friday, September 24, 2010 - 10:47:47 AM

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  • HAL Id : inria-00114888, version 4

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Remi Abgrall. Construction of simple, stable and convergent high order schemes for steady first order Hamilton Jacobi equations.. [Research Report] RR-6055, INRIA. 2006, pp.34. ⟨inria-00114888v4⟩

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