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$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem

$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem
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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.

Author Details

Yidu Yang

Jiayu Han

Hai Bi

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