Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 646–669
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 $H^1$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-10054
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 646–669
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Prescribed curvature equation finite element method Newton iteration Banach fixed-point theorem.