Numerical solution of unsteady elastic equations with C-Bézier basis functions

In this paper, the finite element method is applied to solve the unsteady elastic equations, C-Bézier basis functions are used to construct the shape function spaces, the semi-discrete scheme of the unsteady elastic equations is obtained by Galerkin finite element method and then the fully discretized Galerkin method is obtained by further discretizing the time variable with $\theta$-scheme finite difference. Furthermore, for several numerical examples, the accuracy of approximate solutions are improved by 1–3 order-of magnitudes compared with the Lagrange basis function in $L^{\mathrm{\infty }}$ norm, $L^2$ norm and $H^1$ semi-norm, and the numerical examples show that the method proposed possesses a faster convergence rate. It is fully demonstrated that the C-Bézier basis functions have a better approximation effect in simulating unsteady elastic equations.