TY - JOUR
T1 - Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation
AU - Yang , Yan
AU - Zhang , Shiquan
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1279
EP - 1304
PY - 2018
DA - 2018/07
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2017-0280
UR - https://global-sci.org/intro/article_detail/aamm/12599.html
KW - Mixed finite element, elastodynamics, symmetric formulation, robust error estimates.
AB - <p style="text-align: justify;">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&nbsp;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.</p>