Three-scale convergence for processes in heterogeneous media
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2012
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| In: |
Applicable analysis
Year: 2012, Volume: 91, Issue: 7, Pages: 1351-1373 |
| ISSN: | 1563-504X |
| DOI: | 10.1080/00036811.2011.569498 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1080/00036811.2011.569498 Verlag, Volltext: http://www.tandfonline.com/doi/full/10.1080/00036811.2011.569498?scroll=top&needAccess=true 
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| Author Notes: | D. Trucu, M.A.J. Chaplain, A. Marciniak-Czochra |
| Summary: | 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. |
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| Item Description: | Published online: 15 Apr 2011 Gesehen am 16.08.2017 |
| Physical Description: | Online Resource |
| ISSN: | 1563-504X |
| DOI: | 10.1080/00036811.2011.569498 |