A finite element method for the one-dimensional prescribed curvature problem

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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

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International Journal of Numerical Analysis and Modeling

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