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Pré-Publication, Document De Travail Année : 2024

Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with L1 data

Mirella Aoun
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Olivier Guibé

Résumé

In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and L 1 data. To deal with the non-coercive character of the equation and the low regularity of the right hand-side we mix the finite volume tools and the renormalized techniques. To handle the Neumann boundary conditions we choose solutions having a null median and we prove a convergence result. We present also some numerical experiments in dimension $2$ to illustrate the rate of convergence.
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Dates et versions

hal-03674184 , version 1 (20-05-2022)
hal-03674184 , version 2 (18-06-2024)

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Citer

Mirella Aoun, Olivier Guibé. Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with L1 data. 2024. ⟨hal-03674184v2⟩
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