$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem (Communications in Computational Physics, 2020)
The elastic transmission eigenvalue problem has important applications inthe 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 $H^2$-conforming finite element method andthe spectral element method, and establish the two-grid discretization scheme. Theoretical analysis and numerical experiments show that the methods presented in thispaper can efficiently compute real and complex elastic transmission eigenvalues.