Communication Dans Un Congrès Année : 2020

On the $L^2$ Stability of Finite Volumes for Stationary First Order Systems

Résumé

The aim of this paper is two-folds. Firstly we study first order stationary systems of PDEs of the form $\sum_k A_k\partial_k U + KU = 0$ with $K_\eta tr0$ on $R^d$ . We prove that the classical assumption $K > 0$ is not necessary for the well-posedness of the system and is violated in the particular case of the first order Poisson problem. Secondly we prove the $L^2$ stability of the finite volume discretisations provided the term KU is appropriately discretised on faces. Our result relies on a discrete Gagliardo-Nirenberg-Sobolev inequality to be submitted.
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Dates et versions

cea-04387837 , version 1 (11-01-2024)

Identifiants

Citer

Michaël Ndjinga, Sédrick Kameni Ngwamou. On the $L^2$ Stability of Finite Volumes for Stationary First Order Systems. Finite Volumes for Complex Applications IX (FVCA 9), Jun 2020, Bergen (virtual), Norway. pp.415-423, ⟨10.1007/978-3-030-43651-3_38⟩. ⟨cea-04387837⟩
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