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Convergence of a finite volume scheme for the convection-diffusion equation with L1 data
Université de Provence. (LATP CNRS)
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). (CTL)
Institut de Sûreté et de Radioprotection Nucléaire. (DPAM/SEMIC/LIMSI)
2012 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 81, no 279, 1429-1454 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we prove the convergence of a finite-volume schemefor the time-dependent convection–diffusion equation with an L1 right-handside. To this purpose, we first prove estimates for the discrete solution andfor its discrete time and space derivatives. Then we show the convergence of asequence of discrete solutions obtained with more and more refined discretiza-tions, possibly up to the extraction of a subsequence, to a function which metsthe regularity requirements of the weak formulation of the problem; to thispurpose, we prove a compactness result, which may be seen as a discrete ana-logue to Aubin-Simon’s lemma. Finally, such a limit is shown to be indeed aweak solution.

Place, publisher, year, edition, pages
2012. Vol. 81, no 279, 1429-1454 p.
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-52386DOI: 10.1090/S0025-5718-2011-02571-8ScopusID: 2-s2.0-84870851439OAI: diva2:466357

QP 2012. QC 20130211

Available from: 2011-12-15 Created: 2011-12-15 Last updated: 2013-02-12Bibliographically approved

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Larcher, Aurélien
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Numerical Analysis, NA (closed 2012-06-30)
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