Error Estimates for Semi-Discrete and Fully Discrete Galerkin Finite Element Approximations of the General Linear Second-Order Hyperbolic Equation. (3rd April 2017)

• Record Type: Journal Article
• Authors: Basson, M.; Stapelberg, B.; van Rensburg, N. F. J.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 4(2017)
• Page Start: 466
• Page End: 485
• Publication Date: 2017-04-03
• Subjects: Damped vibration -- error estimates -- finite elements -- Galerkin approximation -- second-order hyperbolic equation; 65M60 -- 65M15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1254655
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In 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.