Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity

作者：Wei, Liang; Li, Zhiping^*

来源：Frontiers of Mathematics in China, 2018, 13(1): 203-226.

DOI：10.1007/s11464-017-0664-x

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

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.

• 出版日期2018-2
• 单位北京大学