Title: A Fourier-Chebyshev Spectral Method for Cavitation Computation in Nonlinear Elasticity,
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.