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Article Dans Une Revue SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada Année : 2019

ON THE WEAK CONSISTENCY OF FINITE VOLUMES SCHEMES FOR CONSERVATION LAWS ON GENERAL MESHES

Résumé

The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, analogues of the Lax-Wendroff theorem for) finite volume schemes for balance laws in the multi-dimensional case and under minimal regularity assumptions for the mesh. As in the seminal Lax-Wendroff paper, our approach relies on a discrete integration by parts of the weak formulation of the scheme. This makes a discrete gradient of the test function appear, and the central argument for the scheme consistency is to remark that this discrete gradient is convergent in L ∞ weak .

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Dates et versions

hal-02055794 , version 1 (04-03-2019)
hal-02055794 , version 2 (05-06-2019)

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Citer

Thierry Gallouët, R. Herbin, J.-C Latché. ON THE WEAK CONSISTENCY OF FINITE VOLUMES SCHEMES FOR CONSERVATION LAWS ON GENERAL MESHES. SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, 2019, 76, pp.581-594. ⟨hal-02055794v2⟩
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