Adv. Appl. Math. Mech., 10 (2018), pp. 1279-1304.
Published online: 2018-07
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0280}, url = {http://global-sci.org/intro/article_detail/aamm/12599.html} }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.