Numerical analysis of oscillations in multiple well problems |
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| Authors: | M Chipot C Collins D Kinderlehrer |
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| Institution: | (1) Département de Mathématiques, Université de Metz, Ile de Saulcy, 57045 Metz-Cedex 01, France , FR;(2) Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA , US;(3) Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA , US |
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| Abstract: | Summary. 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.
Received May 18, 1994 |
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| Keywords: | Mathematics Subject Classification (1991): 65N15 65N30 35J20 35J70 |
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