scholarly journals Existence and non-existence of Schwarz symmetric ground states for elliptic eigenvalue problems

2005 ◽  
Vol 184 (3) ◽  
pp. 297-314 ◽  
Author(s):  
H. Hajaiej ◽  
C.A. Stuart
Keyword(s):  
Eigenvalue Problems ◽  
Ground States ◽  
Elliptic Eigenvalue Problems

scholarly journals A Class of Spectral Element Methods and Its A Priori/A Posteriori Error Estimates for 2nd-Order Elliptic Eigenvalue Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Jiayu Han ◽  
Yidu Yang
Keyword(s):  
Spectral Methods ◽  
Eigenvalue Problems ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Spectral Element ◽  
A Posteriori ◽  
Spectral Element Methods ◽  
A Posteriori Error ◽  
Elliptic Eigenvalue Problems

This paper discusses spectral and spectral element methods with Legendre-Gauss-Lobatto nodal basis for general 2nd-order elliptic eigenvalue problems. The special work of this paper is as follows. (1) We prove a priori and a posteriori error estimates for spectral and spectral element methods. (2) We compare between spectral methods, spectral element methods, finite element methods and their derivedp-version,h-version, andhp-version methods from accuracy, degree of freedom, and stability and verify that spectral methods and spectral element methods are highly efficient computational methods.

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