Second-Order Error Estimates for Piecewise Linear Approximation in One Dimension

In this paper, we consider errors for piecewise linear continuous approximations to smooth one-dimensional curves in . It is shown that simple error estimates based on curvature can be rather accurate: second-order accurate provided nodal values are fourth-order accurate or higher. The estimates are computable with the knowledge of the first derivative of the parametrization of the curves. Numerical tests that verify the accuracy are given. Possible applications are discussed