scholarly journals Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods

2009 ◽  
Vol 54 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Shanghui Jia ◽  
Hehu Xie ◽  
Xiaobo Yin ◽  
Shaoqin Gao
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Finite Element Methods ◽  
Nonconforming Finite Element ◽  
Stokes Eigenvalue Problem ◽  
Nonconforming Finite Element Methods

A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods

2015 ◽  
Vol 8 (3) ◽  
pp. 383-405 ◽  
Author(s):  
Xiaole Han ◽  
Yu Li ◽  
Hehu Xie
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Finite Element Methods ◽  
Correction Method ◽  
Nonconforming Finite Element ◽  
Element Space ◽  
Correction Scheme ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Nonconforming Finite Element Methods

AbstractIn 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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