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A numerical method for detecting singular minimizers (1987)

Ball, J. M. ; Knowles, G.

Springer

Numerische Mathematik 51 (1987), S. 181-197

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Details

ISSN: 0945-3245

Schlagwort(e): AMS(MOS): Primary 65k10 ; 49A10 ; 49D99 ; Secondary 73G05 ; CR: G1.6

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Summary 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01396748

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