Three-scale convergence for processes in heterogeneous media

• Verfasst von: Trucu, Dumitru [VerfasserIn]
• Verfasst von: Chaplain, Mark [VerfasserIn]
• Verfasst von: Marciniak-Czochra, Anna [VerfasserIn]
• Titel: Three-scale convergence for processes in heterogeneous media
• Verf.angabe: D. Trucu, M.A.J. Chaplain, A. Marciniak-Czochra
• Umfang: 23 S.
• Fussnoten: Published online: 15 Apr 2011 ; Gesehen am 16.08.2017
• Titel Quelle: Enthalten in: Applicable analysis
• Jahr Quelle: 2012
• Band/Heft Quelle: 91(2012), 7, S. 1351-1373
• ISSN Quelle: 1563-504X
• DOI: doi:10.1080/00036811.2011.569498
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1562459406

Abstract

In this article, we propose a new notion of multiscale convergence, called ‘three-scale’, which aims to give a topological framework in which to assess complex processes occurring at three different scales or levels within a heterogeneous medium. This generalizes and extends the notion of two-scale convergence, a well-established concept that is now commonly used for obtaining an averaged, asymptotic value (homogenization) of processes that exist on two different spatial scales. The well-posedness of this new concept is justified via a compactness theorem which ensures that all bounded sequences in L 2(Ω) are relative compact with respect to the three-scale convergence. This is taken further by giving a boundedness characterization of three-scale convergent sequences and is then continued with the introduction of the notion of ‘strong three-scale convergence’ whose well-posedness is also discussed. Finally, the three-scale convergence of the gradients is established.