Galerkin finite element approximation of general linear second order hyperbolic equations

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Authors

Basson, Madelein
Van Rensburg, N.F.J.

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Taylor & Francis

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] 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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Citation

Basson, M & Van Rensburg, NFJ 2013, 'Galerkin finite element approximation of general linear second order hyperbolic equations', Numerical Functional Analysis and Optimization, vol. 34, no. 9, pp. 976-1000.