Local a priori/a posteriori error estimates of conforming finite elements approximation for Steklov eigenvalue problems

2013 ◽  
Vol 57 (6) ◽  
pp. 1319-1329 ◽  
Author(s):  
YiDu Yang ◽  
Hai Bi
Keyword(s):  
Finite Elements ◽  
Error Estimates ◽  
Eigenvalue Problems ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problems

scholarly journals A Type of Multigrid Method Based on the Fixed-Shift Inverse Iteration for the Steklov Eigenvalue Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Feiyan Li ◽  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Inverse Iteration ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem

For the Steklov eigenvalue problem, we establish a type of multigrid discretizations based on the fixed-shift inverse iteration and study in depth its a priori/a posteriori error estimates. In addition, we also propose an adaptive algorithm on the basis of the a posteriori error estimates. Finally, we present some numerical examples to validate the efficiency of our method.

scholarly journals A Priori and A Posteriori Error Estimates for a Crank Nicolson Type Scheme of an Elliptic Problem with Dynamical Boundary Conditions

2016 ◽  
Vol 8 (2) ◽  
pp. 1
Author(s):  
Rola Ali Ahmad ◽  
Toufic El Arwadi ◽  
Houssam Chrayteh ◽  
Jean-Marc Sac-Epee
Keyword(s):  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Time Discretization ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Dynamical Boundary Conditions ◽  
Error Indicators ◽  
Crank Nicolson

In this article we claim that we are going to give a priori and a posteriori error estimates for a Crank Nicolson type scheme. The problem is discretized by the finite elements in space. The main result of this paper consists in establishing two types of error indicators, the first one linked to the time discretization and the second one to the space discretization.

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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