@Article{IJNAM-14-646,
author = {Susanne C. Brenner, Li-Yeng Sung, Zhuo Wang and Yuesheng Xu},
title = {A Finite Element Method for the One-Dimensional Prescribed Curvature Problem},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2017},
volume = {14},
number = {4-5},
pages = {646--669},
abstract = {<p style="text-align: justify;">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 $H^1$ norm and the $L^2$ 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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/10054.html}
}