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NUMERICAL SOLUTION OF NONLINEAR ELASTICITY PROBLEMS WITH LAVRENTIEV PHENOMENON

YU BAI

LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P.R.China

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and

ZHIPING LI

LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P.R.China

Corresponding author.

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https://doi.org/10.1142/S0218202507002406Cited by:6 (Source: Crossref)

Abstract

A convergence theory is established for a truncation method in solving polyconvex elasticity problems involving the Lavrentiev phenomenon. Numerical results on a recent example by Foss et al., which has a polyconvex integrand and admits continuous singular minimizers, not only verify our convergence theorems but also provide a sharper estimate on the upper bound of a perturbation parameter for the existence of the Lavrentiev phenomenon in the example.

Keywords:

AMSC: 65K10, 65N30, 49A10

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