CONVERGENCE OF A FINITE VOLUME SCHEME FOR THE CONVECTION-DIFFUSION EQUATION WITH L 1 DATA

Thierry Gallouët (1) , Aurélien Larcher (2) , Jean-Claude Latché (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 IRSN - Institut de Radioprotection et de Sûreté Nucléaire

In this paper, we prove the convergence of a finite-volume scheme for the time-dependent convection–diffusion equation with an L 1 right-hand side. To this purpose, we first prove estimates for the discrete solution and for its discrete time and space derivatives. Then we show the convergence of a sequence of discrete solutions obtained with more and more refined discretiza-tions, possibly up to the extraction of a subsequence, to a function which mets the regularity requirements of the weak formulation of the problem; to this purpose, we prove a compactness result, which may be seen as a discrete analogue to Aubin-Simon's lemma. Finally, such a limit is shown to be indeed a weak solution.

Domaines: Analyse classique [math.CA]

Thierry Gallouët, Aurélien Larcher, Jean-Claude Latché. CONVERGENCE OF A FINITE VOLUME SCHEME FOR THE CONVECTION-DIFFUSION EQUATION WITH L 1 DATA. Mathematics of Computation, 2012, 81 (279), ⟨10.1090/S0025-5718-2011-02571-8⟩. ⟨hal-01283569⟩