Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity

doi:10.1007/s11464-017-0664-x

Front. Math. China

2018, Vol. 13

Issue (1) : 203-226 https://doi.org/10.1007/s11464-017-0664-x

RESEARCH ARTICLE

Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity

Liang WEI, Zhiping LI(

)

LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, China

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Abstract

A Fourier-Chebyshev spectral method is proposed in this paper for solving the cavitation problem in nonlinear elasticity. The interpolation error for the cavitation solution is analyzed, the elastic energy error estimate for the discrete cavitation solution is obtained, and the convergence of the method is proved. An algorithm combined a gradient type method with a damped quasi-Newton method is applied to solve the discretized nonlinear equilibrium equations. Numerical experiments show that the Fourier-Chebyshev spectral method is efficient and capable of producing accurate numerical cavitation solutions.

Keywords Fourier-Chebyshev spectral method cavitation computation nonlinear elasticity interpolation error analysis energy error estimate convergence

Corresponding Author(s): Zhiping LI

Issue Date: 12 January 2018

Cite this article:

Liang WEI,Zhiping LI. Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity[J]. Front. Math. China, 2018, 13(1): 203-226.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0664-x
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I1/203

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