A numerical method for detecting singular minimizers

J. M. Ball; G. Knowles

doi:10.1007/BF01396748

A numerical method for detecting singular minimizers

J. M. Ball, G. Knowles

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

38 Citations (Scopus)

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 language	English
Pages (from-to)	181-197
Number of pages	17
Journal	Numerische Mathematik
Volume	51
Issue number	2
DOIs	https://doi.org/10.1007/BF01396748
Publication status	Published - Mar 1987

Keywords

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

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10.1007/BF01396748

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AB - 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.

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A numerical method for detecting singular minimizers

Abstract

Keywords

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