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

Yan Yang and Shiquan Zhang

10.4208/aamm.OA-2017-0280

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

Preview Full PDF BiBTex 5 830
  • 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.

  • History

Published online: 2018-07

  • Cited by