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Volume 11, Issue 4
Local and Parallel Finite Element Schemes for the Elastic Transmission Eigenvalue Problem

Hai Bi, Jiayu Han & Yidu Yang

DOI: 10.4208/eajam.270720.030621

East Asian J. Appl. Math., 11 (2021), pp. 829-858.

Published online: 2021-08

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  • Abstract

Local and parallel finite element computations for the elastic transmission eigenvalue problem are studied in this paper. After deriving the local a priori error estimates for finite element approximations of the problem, we establish local and parallel finite element schemes, which include classical conforming finite elements and spectral elements for the problem with local low smooth eigenfunctions. The errors of the method are analysed and numerical examples show the efficiency of the schemes.

  • Keywords

Elastic transmission eigenvalue problem, local a priori error estimate, local and parallel scheme, local defect correction.

  • AMS Subject Headings

65N25, 65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-829, author = {Bi , HaiHan , Jiayu and Yang , Yidu}, title = {Local and Parallel Finite Element Schemes for the Elastic Transmission Eigenvalue Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {4}, pages = {829--858}, abstract = {

Local and parallel finite element computations for the elastic transmission eigenvalue problem are studied in this paper. After deriving the local a priori error estimates for finite element approximations of the problem, we establish local and parallel finite element schemes, which include classical conforming finite elements and spectral elements for the problem with local low smooth eigenfunctions. The errors of the method are analysed and numerical examples show the efficiency of the schemes.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.270720.030621}, url = {http://global-sci.org/intro/article_detail/eajam/19374.html} }
TY - JOUR T1 - Local and Parallel Finite Element Schemes for the Elastic Transmission Eigenvalue Problem AU - Bi , Hai AU - Han , Jiayu AU - Yang , Yidu JO - East Asian Journal on Applied Mathematics VL - 4 SP - 829 EP - 858 PY - 2021 DA - 2021/08 SN - 11 DO - http://doi.org/10.4208/eajam.270720.030621 UR - https://global-sci.org/intro/article_detail/eajam/19374.html KW - Elastic transmission eigenvalue problem, local a priori error estimate, local and parallel scheme, local defect correction. AB -

Local and parallel finite element computations for the elastic transmission eigenvalue problem are studied in this paper. After deriving the local a priori error estimates for finite element approximations of the problem, we establish local and parallel finite element schemes, which include classical conforming finite elements and spectral elements for the problem with local low smooth eigenfunctions. The errors of the method are analysed and numerical examples show the efficiency of the schemes.

Bi , HaiHan , Jiayu and Yang , Yidu. (2021). Local and Parallel Finite Element Schemes for the Elastic Transmission Eigenvalue Problem. East Asian Journal on Applied Mathematics. 11 (4). 829-858. doi:10.4208/eajam.270720.030621
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