Basson, MadeleinStapelberg, BelindaJanse van Rensburg, N.F. (Nicolaas)2018-01-192017-04M. Basson, B. Stapelberg & N. F. J. van Rensburg (2017) Error Estimates for Semi-Discrete and Fully Discrete Galerkin Finite Element Approximations of the General Linear Second-Order Hyperbolic Equation, Numerical Functional Analysis and Optimization, 38:4, 466-485, DOI: 10.1080/01630563.2016.1254655.0163-0563 (print)1532-2467 (online)10.1080/01630563.2016.1254655http://hdl.handle.net/2263/63641In this article, we derive error estimates for the semi-discrete and fully discrete Galerkin approximations of a general linear second-order hyperbolic partial differential equation with general damping (which includes boundary damping). The results can be applied to a variety of cases (e.g. vibrating systems of linked elastic bodies). The results generalize pioneering work of Dupont and complement a recent article by Basson and Van Rensburg.en© 2017 Taylor & Francis. This is an electronic version of an article published in Numerical Functional Analysis and Optimization, vol. 38, no. 4, pp.466-485, 2017. doi : 10.1080/01630563.2016.1254655. Numerical Functional Analysis and Optimization is available online at : http://www.tandfonline.comloi/lnfa20.Damped vibrationSecond-order hyperbolic equationError estimatesFinite elementsGalerkin approximationBoundary conditionsBeamWave equationPostprint Article