Title
A finite element method for the one-dimensional prescribed curvature problem
Document Type
Article
Publication Date
1-1-2017
Abstract
We develop a finite element method for solving the Dirichlet problem of the one-dimensional prescribed curvature equation due to its irreplaceable role in applications. Specifically, we first analyze the existence and uniqueness of the solution of the problem and then develop a finite element method to solve it. The well-posedness of the finite element method is shown by employing the Banach fixed-point theorem. The optimal error estimates of the proposed method in both the H norm and the L norm are established. We also design a Newton type iteration scheme to solve the resulting discrete nonlinear system. Numerical experiments are presented to confirm the order of convergence of the proposed method. 1 2
Publication Source (Journal or Book title)
International Journal of Numerical Analysis and Modeling
First Page
646
Last Page
669
Recommended Citation
Brenner, S., Sung, L., Wang, Z., & Xu, Y. (2017). A finite element method for the one-dimensional prescribed curvature problem. International Journal of Numerical Analysis and Modeling, 14 (4-5), 646-669. Retrieved from https://repository.lsu.edu/mathematics_pubs/122