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Numerical analysis of oscillations in multiple well problems


Chipot, M; Collins, C; Kinderlehrer, D (1995). Numerical analysis of oscillations in multiple well problems. Numerische Mathematik, 70(3):259-282.

Abstract

Variational problems which fail to be convex occur often in the study of ordered materials such as crystals. In these problems, the energy density for the material has multiple potential wells. In this paper, we study multiple-well problems by first determining the analytic properties of energy minimizing sequences and then by estimating the continuous problem by an approximation using piecewise linear finite elements. We show that even when there is no minimizer of the energy, the approximations still take on a predictable structure.

Abstract

Variational problems which fail to be convex occur often in the study of ordered materials such as crystals. In these problems, the energy density for the material has multiple potential wells. In this paper, we study multiple-well problems by first determining the analytic properties of energy minimizing sequences and then by estimating the continuous problem by an approximation using piecewise linear finite elements. We show that even when there is no minimizer of the energy, the approximations still take on a predictable structure.

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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:Galerkin methods; error bounds; numerical example; variational methods; oscillations; multiple well problems; non-convex variational problems; Young measure; finite element method
Language:English
Date:1995
Deposited On:26 Aug 2010 09:38
Last Modified:06 Dec 2017 21:06
Publisher:Springer
ISSN:0029-599X
Publisher DOI:https://doi.org/10.1007/s002110050119
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0824.65045

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