@Article{IJNAM-14-4-5, author = {}, 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 = {
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.
}, issn = {2617-8710}, doi = {https://doi.org/2017-IJNAM-10054}, url = {https://global-sci.com/article/83195/a-finite-element-method-for-the-one-dimensional-prescribed-curvature-problem} }