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Numerical approximations in variational problems with potential wells


Chipot, M; Collins, C (1992). Numerical approximations in variational problems with potential wells. SIAM Journal on Numerical Analysis, 29(4):1002-1019.

Abstract

In this paper, some numerical aspects of variational problems which fail to be convex are studied. It is well known that for such a problem, in general, the infimum of the energy (the functional that has to be minimized) fails to be attained. Instead, minimizing sequences develop oscillations which allow them to decrease the energy.It is shown that there exists a minimizes for an approximation of the problem and the oscillations in the minimizing sequence are analyzed. It is also shown that these minimizing sequences choose their gradients in the vicinity of the wells with a probability which tends to be constant. An estimate of the approximate deformation as it approximates a measure and some numerical results are also given. ©1992 Society for Industrial and Applied Mathematics

In this paper, some numerical aspects of variational problems which fail to be convex are studied. It is well known that for such a problem, in general, the infimum of the energy (the functional that has to be minimized) fails to be attained. Instead, minimizing sequences develop oscillations which allow them to decrease the energy.It is shown that there exists a minimizes for an approximation of the problem and the oscillations in the minimizing sequence are analyzed. It is also shown that these minimizing sequences choose their gradients in the vicinity of the wells with a probability which tends to be constant. An estimate of the approximate deformation as it approximates a measure and some numerical results are also given. ©1992 Society for Industrial and Applied Mathematics

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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:finite element method, variational problem, Young measure
Language:English
Date:1992
Deposited On:31 Aug 2010 09:07
Last Modified:05 Apr 2016 13:28
Publisher:Society for Industrial and Applied Mathematics
ISSN:0036-1429
Additional Information:©1992 Society for Industrial and Applied Mathematics
Publisher DOI:10.1137/0729061
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0763.65049
Permanent URL: http://doi.org/10.5167/uzh-22731

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