Convergence of the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography
| Autor: | Xavier Lhébrard, François Bouchut |
|---|---|
| Přispěvatelé: | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2020 |
| Předmět: |
kinetic function Mathematics
Inverse Geometry 010103 numerical & computational mathematics hydrostatic reconstruction Kinetic energy 01 natural sciences law.invention MSC: 65M12 76M12 35L65 Square root law well-balanced scheme [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Entropy (information theory) 0101 mathematics Mathematics convergence Algebra and Number Theory Applied Mathematics Mathematical analysis Dissipation Lipschitz continuity Saint Venant system with topography 010101 applied mathematics Computational Mathematics Bounded function entropy inequality Hydrostatic equilibrium [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Mathematics of Computation Mathematics of Computation, American Mathematical Society, 2021, 90 (329), pp.1119-1153. ⟨10.1090/mcom/3600⟩ |
| ISSN: | 1088-6842 0025-5718 |
| DOI: | 10.1090/mcom/3600 |
| Popis: | International audience; We prove the convergence of the hydrostatic reconstruction scheme with kinetic numerical flux for the Saint Venant system with Lipschitz continuous topography. We use a recently derived fully discrete sharp entropy inequality with dissipation, that enables us to establish an estimate in the inverse of the square root of the space increment ∆x of the L 2 norm of the gradient of approximate solutions. By Diperna's method we conclude the strong convergence towards bounded weak entropy solutions. |
| Databáze: | OpenAIRE |
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