Quasi-norm a priori and a posteriori error estimates for the nonconforming approximation of p-Laplacian

2001 ◽  
Vol 89 (2) ◽  
pp. 341-378 ◽  
Author(s):  
Wenbin Liu ◽  
Ningning Yan
Keyword(s):  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error

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 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.

scholarly journals A Priori and a Posteriori Error Estimates of a WOPSIP DG Method for the Heat Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yuping Zeng ◽  
Kunwen Wen ◽  
Fen Liang ◽  
Huijian Zhu
Keyword(s):  
Heat Equation ◽  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Fully Discrete ◽  
Backward Euler ◽  
Elliptic Reconstruction

We introduce and analyze a weakly overpenalized symmetric interior penalty method for solving the heat equation. We first provide optimal a priori error estimates in the energy norm for the fully discrete scheme with backward Euler time-stepping. In addition, we apply elliptic reconstruction techniques to derive a posteriori error estimators, which can be used to design adaptive algorithms. Finally, we present two numerical experiments to validate our theoretical analysis.

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.

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