Convergence of a finite volume scheme for the convection-diffusion equation with $\mathrm {L}^1$ data
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- by T. Gallouët, A. Larcher and J. C. Latché PDF
- Math. Comp. 81 (2012), 1429-1454 Request permission
Abstract:
In this paper, we prove the convergence of a finite-volume scheme for the time-dependent convection–diffusion equation with an $\mathrm {L}^1$ 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 discretizations, possibly up to the extraction of a subsequence, to a function which meets 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 the Aubin-Simon lemma. Finally, such a limit is shown to be indeed a weak solution.References
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Additional Information
- T. Gallouët
- Affiliation: Université de Provence, France
- Email: gallouet@cmi.univ-mrs.fr
- A. Larcher
- Affiliation: Institut de Radioprotection et de Sûreté Nucléaire (IRSN), France
- Email: aurelien.larcher@grriai.com
- J. C. Latché
- Affiliation: Institut de Radioprotection et de Sûreté Nucléaire (IRSN), France
- MR Author ID: 715367
- Email: jean-claude.latche@irsn.fr
- Received by editor(s): July 23, 2010
- Received by editor(s) in revised form: April 18, 2011
- Published electronically: December 21, 2011
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1429-1454
- MSC (2010): Primary 35K10, 65M12, 65M08
- DOI: https://doi.org/10.1090/S0025-5718-2011-02571-8
- MathSciNet review: 2904585