Volume 10, Issue 5
Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation

Yan Yang & Shiquan Zhang

Adv. Appl. Math. Mech., 10 (2018), pp. 1279-1304.

Published online: 2018-07

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  • 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 L2 norm for stress, and the L2norm 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 Lame constant λ. The stress approximation in both norms, as well as the velocity approximation in L2 norm, are with optimal convergence order. Finally numerical experiments are provided to confirm the theoretical analysis.

  • Keywords

Mixed finite element elastodynamics symmetric formulation robust error estimates.

  • AMS Subject Headings

65N15 65N30 74H15 74S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-1279, author = {Yan Yang and Shiquan Zhang}, title = {Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {5}, pages = {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 L2 norm for stress, and the L2norm 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 Lame constant λ. The stress approximation in both norms, as well as the velocity approximation in L2 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} }
TY - JOUR T1 - Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation AU - Yan Yang & Shiquan Zhang JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1279 EP - 1304 PY - 2018 DA - 2018/07 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0280 UR - https://global-sci.org/intro/article_detail/aamm/12599.html KW - Mixed finite element KW - elastodynamics KW - symmetric formulation KW - robust error estimates. AB -

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 L2 norm for stress, and the L2norm 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 Lame constant λ. The stress approximation in both norms, as well as the velocity approximation in L2 norm, are with optimal convergence order. Finally numerical experiments are provided to confirm the theoretical analysis.

Yan Yang & Shiquan Zhang. (1970). Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation. Advances in Applied Mathematics and Mechanics. 10 (5). 1279-1304. doi:10.4208/aamm.OA-2017-0280
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