scholarly journals A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem

2020 ◽  
Vol 83 (3) ◽  
Author(s):  
Yingxia Xi ◽  
Xia Ji ◽  
Shuo Zhang
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
High Accuracy ◽  
Nonconforming Finite Element ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem

scholarly journals An Adaptive Finite Element Scheme for the Hellinger–Reissner Elasticity Mixed Eigenvalue Problem

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Fleurianne Bertrand ◽  
Daniele Boffi ◽  
Rui Ma
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Degrees Of Freedom ◽  
Elasticity Problem ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Mixed Eigenvalue

Abstract In this paper, we study the approximation of eigenvalues arising from the mixed Hellinger–Reissner elasticity problem by using a simple finite element introduced recently by one of the authors. We prove that the method converges when a residual type error estimator is considered and that the estimator decays optimally with respect to the number of degrees of freedom. A postprocessing technique originally proposed in a different context is discussed and tested numerically.

Nonconforming Finite Element Method for the Transmission Eigenvalue Problem

2016 ◽  
Vol 9 (1) ◽  
pp. 92-103 ◽  
Author(s):  
Xia Ji ◽  
Yingxia Xi ◽  
Hehu Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonconforming Finite Element ◽  
Transmission Eigenvalues ◽  
Nonconforming Finite Element Method ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem ◽  
Eigenvalue And Eigenfunction ◽  
Theoretical Results ◽  
Element Method

AbstractIn this paper, we analyze a nonconforming finite element method for the computation of transmission eigenvalues and the corresponding eigenfunctions. The error estimates of the eigenvalue and eigenfunction approximation are given, respectively. Finally, some numerical examples are provided to validate the theoretical results.

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