A finite difference scheme for conservation laws driven by Lévy noise
| Jazyk: | English |
|---|---|
| ISSN: | 0272-4979 1464-3642 |
| DOI: | 10.1093/imanum/drx023⟩ |
| Přístupová URL adresa: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::77c620e325b0aef4cb79c904c12b86d8 https://hal.archives-ouvertes.fr/hal-02134602 |
| Rights: | OPEN |
| Přírůstkové číslo: | edsair.doi.dedup.....77c620e325b0aef4cb79c904c12b86d8 |
| Autor: | Ananta K. Majee, Guy Vallet, Ujjwal Koley |
| Přispěvatelé: | Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Conservation law
Sequence Applied Mathematics General Mathematics 010102 general mathematics Multiplicative function Numerical Analysis (math.NA) Expected value 01 natural sciences 010101 applied mathematics Computational Mathematics Entropy (classical thermodynamics) Levy noise Mathematics - Analysis of PDEs Homogeneous FOS: Mathematics Finite difference scheme Applied mathematics Mathematics - Numerical Analysis 0101 mathematics [MATH]Mathematics [math] Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | IMA Journal of Numerical Analysis IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2018, 38 (2), pp.998-1050. ⟨10.1093/imanum/drx023⟩ |
| ISSN: | 0272-4979 1464-3642 |
| DOI: | 10.1093/imanum/drx023⟩ |
| Popis: | In this paper, we analyze a semi-discrete finite difference scheme for a conservation laws driven by a homogeneous multiplicative Levy noise. Thanks to BV estimates, we show a compact sequence of approximate solutions, generated by the finite difference scheme, converges to the unique entropy solution of the underlying problem, as the spatial mesh size \Dx-->0. Moreover, we show that the expected value of the L^1-difference between the approximate solution and the unique entropy solution converges at a rate O(\sqrt{\Dx}). 38 Pages |
| Databáze: | OpenAIRE |
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