@article{Sun2024, 
author = {Lanyin Sun and Kunkun Pang},
title = {Numerical solution of unsteady elastic equations with C-Bézier basis functions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {702-722},
keywords = {unsteady elastic equation, finite element method, C-Bézier basis functions},
url = {https://www.sciopen.com/article/10.3934/math.2024036},
doi = {10.3934/math.2024036},
abstract = {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    θ-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    ∞   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.}
}