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- Title
Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with L1 data.
- Authors
Aoun, Mirella; Guibé, Olivier
- Abstract
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.
- Subjects
NEUMANN problem; NEUMANN boundary conditions; FINITE volume method; RENORMALIZATION (Physics); TRANSPORT equation; NUMERICAL analysis
- Publication
Calcolo, 2024, Vol 61, Issue 3, p1
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-024-00602-3