scholarly journals Conforming Finite Element Approximations for a Fourth-Order Steklov Eigenvalue Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Hai Bi ◽  
Shixian Ren ◽  
Yidu Yang
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Fourth Order ◽  
Finite Element Approximation ◽  
Continuous Operator ◽  
Element Approximation ◽  
Morley Element ◽  
Steklov Eigenvalue ◽  
Conforming Finite Element ◽  
Steklov Eigenvalue Problem

This paper characterizes the spectrum of a fourth-order Steklov eigenvalue problem by using the spectral theory of completely continuous operator. The conforming finite element approximation for this problem is analyzed, and the error estimate is given. Finally, the bounds for Steklov eigenvalues on the square domain are provided by Bogner-Fox-Schmit element and Morley element.

A virtual element method for a biharmonic Steklov eigenvalue problem

2019 ◽  
Vol 10 (4) ◽  
pp. 325-337 ◽  
Author(s):  
Gabriel Monzón
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Fourth Order ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Virtual Element Method ◽  
Eigenvalues And Eigenfunctions ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Virtual Element

AbstractWe propose a finite element approximation for a fourth-order Steklov eigenvalue problem by means of the virtual elements. In this setting we derive error estimates for the eigenvalues and eigenfunctions under standard assumptions on the domain.

scholarly journals Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow

2020 ◽  
Vol 30 (05) ◽  
pp. 847-865
Author(s):  
Gabriel Barrenechea ◽  
Erik Burman ◽  
Johnny Guzmán
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Inviscid Flow ◽  
Element Approximation ◽  
Well Posedness ◽  
Hodge Laplacian ◽  
Conforming Finite Element ◽  
Velocity Approximation

We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using [Formula: see text](div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the [Formula: see text]-norm of order [Formula: see text]. We also prove error estimates for the pressure error in the [Formula: see text]-norm.

On a fourth order Steklov eigenvalue problem

Analysis ◽  
2005 ◽  
Vol 25 (4) ◽  
Author(s):  
Alberto Ferrero ◽  
Filippo Gazzola ◽  
Tobias Weth
Keyword(s):  
Eigenvalue Problem ◽  
Bounded Domain ◽  
Fourth Order ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem

SummaryWe study the spectrum of a biharmonic Steklov eigenvalue problem in a bounded domain of R

A Posteriori Error Estimates for a Steklov Eigenvalue Problem

2012 ◽  
Vol 557-559 ◽  
pp. 2081-2086 ◽  
Author(s):  
Ling Ling Sun ◽  
Yi Du Yang
Keyword(s):  
Eigenvalue Problem ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Error Estimator ◽  
Element Approximation ◽  
A Posteriori ◽  
Validity And Reliability ◽  
A Posteriori Error ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem

This paper discusses the finite element approximation for a Steklov eigenvalue problem. Based on the work of Armentano and Padra ( Appl Numer Math 58 (2008) 593-601), an a posteriori error estimator is provided and its validity and reliability are proved theoretically. Finally, numerical experiments with Matlab program are carried out to confirm the theoretical analysis.

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