Year: 2018
Author: Yan Yang, Shiquan Zhang
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 5 : pp. 1279–1304
Abstract
In this paper, we analyze semi-discrete and fully discrete mixed finite element methods for linear elastodynamics problems in the symmetric formulation. For a large class of conforming mixed finite element methods, the error estimates for each scheme are derived, including the energy norm and $L^2$ norm for stress, and the $L^2$ norm for velocity. All the error estimates are robust for the nearly incompressible materials, in the sense that the constant bound and convergence order are independent of Lamé constant λ. The stress approximation in both norms, as well as the velocity approximation in $L^2$ norm, are with optimal convergence order. Finally numerical experiments are provided to confirm the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2017-0280
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 5 : pp. 1279–1304
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Mixed finite element elastodynamics symmetric formulation robust error estimates.