Volume 8, Issue 3
A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods

Xiaole Han, Yu Li & Hehu Xie

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 383-405.

Published online: 2015-08

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  • Abstract

In this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This correction scheme can increase the overall efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, as same as the direct eigenvalue solving by nonconforming finite element methods, this multilevel correction method can also produce the lower-bound approximations of the eigenvalues.

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@Article{NMTMA-8-383, author = {}, title = {A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {3}, pages = {383--405}, abstract = {

In this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This correction scheme can increase the overall efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, as same as the direct eigenvalue solving by nonconforming finite element methods, this multilevel correction method can also produce the lower-bound approximations of the eigenvalues.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1334}, url = {http://global-sci.org/intro/article_detail/nmtma/12415.html} }
TY - JOUR T1 - A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 383 EP - 405 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.m1334 UR - https://global-sci.org/intro/article_detail/nmtma/12415.html KW - AB -

In this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This correction scheme can increase the overall efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, as same as the direct eigenvalue solving by nonconforming finite element methods, this multilevel correction method can also produce the lower-bound approximations of the eigenvalues.

Xiaole Han, Yu Li & Hehu Xie. (2020). A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods. Numerical Mathematics: Theory, Methods and Applications. 8 (3). 383-405. doi:10.4208/nmtma.2015.m1334
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