Convergence of a finite volume scheme for the convection-diffusion equation with L1 data
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
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.
IdentifiersURN: urn:nbn:se:kth:diva-52386DOI: 10.1090/S0025-5718-2011-02571-8ScopusID: 2-s2.0-84870851439OAI: oai:DiVA.org:kth-52386DiVA: diva2:466357
QP 2012. QC 201302112011-12-152011-12-152013-02-12Bibliographically approved