Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation

Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation

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.

Author Details

Yan Yang

Shiquan Zhang