scholarly journals An Adaptive Nonconforming Finite Element Algorithm for Laplace Eigenvalue Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Yuanyuan Yu ◽  
Yidu Yang ◽  
Jiayu Han
Keyword(s):  
Adaptive Algorithm ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Rayleigh Quotient ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Laplace Eigenvalue ◽  
Rayleigh Quotient Iteration ◽  
Element Algorithm

We establish Crouzeix-Raviart element adaptive algorithm based on Rayleigh quotient iteration and give its a priori/a posteriori error estimates. Our algorithm is performed under the package of Chen, and satisfactory numerical results are obtained.

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.

A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method

2013 ◽  
Vol 14 (3) ◽  
pp. 753-779
Author(s):  
Yuping Zeng ◽  
Jinru Chen
Keyword(s):  
Elliptic Problem ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Energy Norm ◽  
Error Estimator ◽  
A Posteriori ◽  
Interior Penalty ◽  
A Posteriori Error ◽  
A Priori Error Estimate

AbstractIn this paper, we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem. An optimal a priori error estimate in the energy norm is proved. In addition, a residual-based a posteriori error estimator is obtained. The estimator is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to demonstrate the effectiveness of our method.

scholarly journals CONVERGENCE AND ERROR ESTIMATES OF TWO ITERATIVE METHODS FOR THE STRONG SOLUTION OF THE INCOMPRESSIBLE KORTEWEG MODEL

2009 ◽  
Vol 19 (09) ◽  
pp. 1713-1742
Author(s):  
F. GUILLÉN-GONZÁLEZ ◽  
M. A. RODRÍGUEZ-BELLIDO
Keyword(s):  
Strong Solution ◽  
Error Estimates ◽  
Fluid Model ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Strong Solutions ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Banach’S Fixed Point Theorem

We show the existence of strong solutions for a fluid model with Korteweg tensor, which is obtained as limit of two iterative linear schemes. The different unknowns are sequentially decoupled in the first scheme and in parallel form in the second one. In both cases, the whole sequences are bounded in strong norms and convergent towards the strong solution of the system, by using a generalization of Banach's fixed point theorem. Moreover, we explicit a priori and a posteriori error estimates (respect to the weak norms), which let us to compare both schemes.

Sign in / Sign up

Export Citation Format

Share Document