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On the determination of limits for some sequences of functions and differential operators
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.ORCID iD: 0000-0001-6742-5781
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.ORCID iD: 0000-0003-2942-6841
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Responsible organisation
2006 (English)In: Canadian Applied Mathematics Quarterly, ISSN 1073-1849, Vol. 14, no 3, 299-329 p.Article in journal (Refereed) Published
Abstract [en]

This article deals with homogenization methods, namely two-scale convergence and Hconvergence, with the aim of comparing their efficiency in studying composite materials. Analytic examples are given to illustrate both methods. While compensated compactness allows one to determine the limit of a product of two weakly converging sequences under additional assumptions on the derivatives, two-scale convergence takes advantage of underlying oscillations of solution sequences and H-convergence is concerned with the operator behaviour. Special attention is paid to periodic homogenization as this case yields the most involved results. Numerical experiments are used to investigate open questions in H-convergence dealing with the possible relaxation of some convergence hypotheses. Partial results are established in this respect.

Place, publisher, year, edition, pages
2006. Vol. 14, no 3, 299-329 p.
Keyword [en]
Two-scale convergence, G-convergence
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-3813Local ID: 4081OAI: oai:DiVA.org:miun-3813DiVA: diva2:28845
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2016-12-12Bibliographically approved

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