$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem
Year: 2020
Author: Yidu Yang, Jiayu Han, Hai Bi
Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1366–1388
Abstract
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 $H^2$-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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0171
Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1366–1388
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Elastic transmission eigenvalues linear weak formulation finite element spectral element the two-grid discretization error estimates.