TY - JOUR
T1 - A Finite Element Method for the One-Dimensional Prescribed Curvature Problem
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 646
EP - 669
PY - 2017
DA - 2017/08
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10054.html
KW - Prescribed curvature equation, finite element method, Newton iteration, Banach fixed-point theorem.
AB - <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>