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Volume 10, Issue 2
Immersed Finite Element Method for Eigenvalue Problems in Elasticity

Seungwoo Lee, Do Young Kwak & Imbo Sim

DOI: 10.4208/aamm.OA-2016-0189

Adv. Appl. Math. Mech., 10 (2018), pp. 424-444.

Published online: 2018-10

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  • Abstract

We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming element. The stability and the optimal convergence of IFEM for solving eigenvalue problems with interface are proved by adopting spectral analysis methods for the classical eigenvalue problem. Numerical experiments demonstrate our theoretical results.

  • Keywords

Immersed finite element, elasticity problem, eigenvalue.

  • AMS Subject Headings

65N30, 65N25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-424, author = {Lee , SeungwooKwak , Do Young and Sim , Imbo}, title = {Immersed Finite Element Method for Eigenvalue Problems in Elasticity}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {2}, pages = {424--444}, abstract = {

We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming element. The stability and the optimal convergence of IFEM for solving eigenvalue problems with interface are proved by adopting spectral analysis methods for the classical eigenvalue problem. Numerical experiments demonstrate our theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0189}, url = {http://global-sci.org/intro/article_detail/aamm/12219.html} }
TY - JOUR T1 - Immersed Finite Element Method for Eigenvalue Problems in Elasticity AU - Lee , Seungwoo AU - Kwak , Do Young AU - Sim , Imbo JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 424 EP - 444 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2016-0189 UR - https://global-sci.org/intro/article_detail/aamm/12219.html KW - Immersed finite element, elasticity problem, eigenvalue. AB -

We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming element. The stability and the optimal convergence of IFEM for solving eigenvalue problems with interface are proved by adopting spectral analysis methods for the classical eigenvalue problem. Numerical experiments demonstrate our theoretical results.

Lee , SeungwooKwak , Do Young and Sim , Imbo. (2018). Immersed Finite Element Method for Eigenvalue Problems in Elasticity. Advances in Applied Mathematics and Mechanics. 10 (2). 424-444. doi:10.4208/aamm.OA-2016-0189
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