## A robust finite element method for elastic vibration problems

- Aug. 31, 2018
- 2:15 p.m.
- LeConte 312

## Abstract

A robust finite element method is introduced for solving elastic vibration problems in two dimensions. The discretization in time is based on the $P _ 1$-continuous discontinuous Galerkin (CDG) method, while the spatial discretization on the Crouziex-Raviart (CR) element. It is proved that the error of the displacement (resp. velocity) in the energy norm (resp. $L^2$ norm) is bounded by $O(h+k)$ (resp. $O(h^2+k)$), where $h$ and $k$ denote the mesh sizes of the subdivisions in space and time, respectively. Under some regularity assumptions on the exact solution, the error bound is independent of the LamÃ© coefficients of the elastic material under discussion. Several numerical results are reported to illustrate numerical performance of the proposed method. This is a joint work with Yuling Guo from Shanghai Jiao Tong University.