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The appearance of microstructures in problems with incompatible wells and their numerical approach


Chipot, M (1999). The appearance of microstructures in problems with incompatible wells and their numerical approach. Numerische Mathematik, 83(3):325-352.

Abstract

The goal of the paper is to analyze the creation of microstructure in problems of Calculus of Variations with wells. More precisely we consider a case with strong incompatibility between the wells. This forces the minimizing sequences to use other gradients than the wells in a puzzling way. Using a method we are then able to single out discrete minimizing sequences and to give energy estimates in terms of the mesh size.

Abstract

The goal of the paper is to analyze the creation of microstructure in problems of Calculus of Variations with wells. More precisely we consider a case with strong incompatibility between the wells. This forces the minimizing sequences to use other gradients than the wells in a puzzling way. Using a method we are then able to single out discrete minimizing sequences and to give energy estimates in terms of the mesh size.

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9 citations in Web of Science®
9 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:microstructures; incompatible wells; oscillations; material science; minimizing sequences; finite element method; energy estimates
Language:English
Date:1999
Deposited On:23 Jul 2010 09:43
Last Modified:05 Apr 2016 13:26
Publisher:Springer
ISSN:0029-599X
Publisher DOI:https://doi.org/10.1007/s002110050452
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1714946
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0937.65070

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