Convection and total variation flow—erratum and improvement
| Autor: | Robert Eymard, François Bouchut, David Doyen |
|---|---|
| Přispěvatelé: | Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Convection
Applied Mathematics General Mathematics entropy formulation 010103 numerical & computational mathematics Mechanics Hyperbolic scalar conservation law 01 natural sciences 1-Laplacian 010101 applied mathematics Computational Mathematics Flow (mathematics) total variation flow finite elements 0101 mathematics Variation (astronomy) finite volumes [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Zdroj: | IMA Journal of Numerical Analysis IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2017, 37 (4), pp.2139-2169. ⟨10.1093/imanum/drw076⟩ |
| ISSN: | 0272-4979 1464-3642 |
| DOI: | 10.1093/imanum/drw076⟩ |
| Popis: | International audience; This paper includes an erratum to (Bouchut et al. (2014) Convection and total variation flow. IMA J. Numer. Anal.,34, 1037–1071.) which deals with a nonlinear hyperbolic scalar conservation law, regularized by the total variation flow operator (or 1-Laplacian), and in which a mistake occurred in the convergence proof of the numerical scheme to the continuous entropy solution. For correcting the proof, it is necessary to introduce an additional vanishing viscous term in the scheme. This modification requires casting the whole paper in the framework of discrete and continuous solutions with unbounded support. This new version, nevertheless, leads to a better result than the previous one, since the bounded variation regularity and the compactness of the support of the initial data are no longer assumed. |
| Databáze: | OpenAIRE |
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