IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

## 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 Lamé 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.

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