TY - JOUR
T1 - $H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem
AU - Yang , Yidu
AU - Han , Jiayu
AU - Bi , Hai
JO - Communications in Computational Physics
VL - 4
SP - 1366
EP - 1388
PY - 2020
DA - 2020/08
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2019-0171
UR - https://global-sci.org/intro/article_detail/cicp/18103.html
KW - Elastic transmission eigenvalues, linear weak formulation, finite element, spectral element, the two-grid discretization, error estimates.
AB - <p style="text-align: justify;">The elastic transmission eigenvalue problem has important applications in
the inverse elastic scattering theory. Recently, the numerical computation for this problem has attracted the attention of the researchers. In this paper, we propose the $H^2$-conforming methods including the classical <span style="text-align: justify;">$H^2$-</span>conforming finite element method and
the spectral element method, and establish the two-grid discretization scheme. Theoretical analysis and numerical experiments show that the methods presented in this
paper can efficiently compute real and complex elastic transmission eigenvalues.</p>