Galerkin Finite Element Approximation of General Linear Second Order Hyperbolic Equations |
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| Authors: | M. Basson N. F. J. van Rensburg |
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| Affiliation: | 1. Department of Mathematics and Applied Mathematics , University of Pretoria , Pretoria , South Africa madelein.basson@up.ac.za;3. Department of Mathematics and Applied Mathematics , University of Pretoria , Pretoria , South Africa |
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| Abstract: | In this article, we derive error estimates for the Galerkin approximation of a general linear second order hyperbolic equation. The results can be applied to a variety of cases, for example, vibrating systems of linked elastic bodies. The results generalize the work of Baker [1 G. A. Baker ( 1976 ). Error estimates for finite element methods for second order hyperbolic equations . SIAM J. Numer. Anal. 13 : 564 – 576 .[Crossref], [Web of Science ®] , [Google Scholar]] and also allow for viscous type damping. Splitting the proofs for the semi-discrete and fully discrete cases not only simplifies the proofs but less restrictive regularity assumptions are required. |
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| Keywords: | Damped vibration Error estimates Finite elements Galerkin approximation Second order hyperbolic equation |
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