A numerical method for detecting singular minimizers

J. M. Ball, G. Knowles

Research output: Contribution to journalArticle

Abstract

A numerical method for computing minimizers in one-dimensional problems of the calculus of variations is described. Such minimizers may have unbounded derivatives, even when the integrand is smooth and regular. In such cases, because of the Lavrentiev phenomenon, standard finite element methods may fail to converge to a minimizer. The scheme proposed is shown to converge to an absolute minimizer and is tested on an example. The effect of quadrature is analyzed. The implications for higher-dimensional problems, and in particular for fracture in nonlinear elasticity, are discussed. © 1987 Springer-Verlag.

Original languageEnglish
Pages (from-to)181-197
Number of pages17
JournalNumerische Mathematik
Volume51
Issue number2
DOIs
Publication statusPublished - Mar 1987

Keywords

  • Subject Classifications: AMS(MOS): Primary 65k10, 49A10, 49D99, Secondary 73G05, CR: G1.6

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