Error estimates of vibrations of elastic string with moving ends

In this work, a mathematical model for small vibrations of an elastic string with moving boundaries is discussed. Global existence and uniqueness of solutions have been established in [M.A. Rincon, I.-S. Liu, Existence and uniqueness of solutions of elastic string with moving ends, Math. Methods Appl. Sci. 27 (14) (2004) 1641–1655]. The objective of this paper is to obtain the error estimates of solutions in Sobolev spaces for the semi-discrete problem, with discretization of space variable and continuous time. The analysis is based on Galerkin finite element method.