CONVERGENCE OF A hp-STREAMLINE DIFFUSION SCHEME FOR VLASOV–FOKKER–PLANCK SYSTEM

2007 ◽  
Vol 17 (08) ◽  
pp. 1159-1182 ◽  
Author(s):  
M. ASADZADEH ◽  
A. SOPASAKIS
Keyword(s):  
Finite Element ◽  
A Priori ◽  
Mesh Size ◽  
Stability Estimates ◽  
Spectral Order ◽  
Element Discretization ◽  
Diffusion Scheme ◽  
Streamline Diffusion ◽  
Stabilization Parameter ◽  
Fokker Planck

We analyze the hp-version of the streamline diffusion finite element method for the Vlasov–Fokker–Planck system. For this method we prove the stability estimates and derive sharp a priori error bounds in a stabilization parameter δ ~ min (h/p, h2/σ), with h denoting the mesh size of the finite element discretization in phase-space-time, p the spectral order of approximation, and σ the transport cross-section.

AN ADAPTIVE FINITE ELEMENT METHOD WITH EFFICIENT MAXIMUM NORM ERROR CONTROL FOR ELLIPTIC PROBLEMS

1994 ◽  
Vol 04 (03) ◽  
pp. 313-329 ◽  
Author(s):  
KENNETH ERIKSSON
Keyword(s):  
Finite Element ◽  
Error Control ◽  
A Priori ◽  
Mesh Size ◽  
Maximum Norm ◽  
Adaptive Finite Element Method ◽  
Local Regularity ◽  
Adaptive Finite Element ◽  
Element Discretization ◽  
Elliptic Model

A posteriori and a priori error estimates are derived for a finite element discretization method applied to an elliptic model problem. The underlying partitions need not be quasi-uniform and can be highly graded; only a certain weak, local mesh regularity is assumed. The error is bounded in terms of the local mesh size and the local regularity of the solution and data. An adaptive algorithm is designed for automatic control of the discretization error in the maximum norm. The error control is proved to be both reliable and efficient.

A TRUNCATED FOURIER/FINITE ELEMENT DISCRETIZATION OF THE STOKES EQUATIONS IN AN AXISYMMETRIC DOMAIN

2006 ◽  
Vol 16 (02) ◽  
pp. 233-263 ◽  
Author(s):  
Z. BELHACHMI ◽  
C. BERNARDI ◽  
S. DEPARIS ◽  
F. HECHT
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Stokes Problem ◽  
A Priori ◽  
Three Dimensional ◽  
Angular Variable ◽  
A Posteriori ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Good Agreement

We consider the Stokes problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian domain. We propose a discretization of this problem which combines Fourier truncation and finite element methods applied to each of the two-dimensional systems. We give the detailed a priori and a posteriori analyses of the discretization and present some numerical experiments which are in good agreement with the analysis.

scholarly journals Brezzi-Pitkaranta stabilization and a priori error analysis for the Stokes Control

2016 ◽  
Vol 7 (1) ◽  
pp. 75-82
Author(s):  
Aytekin Cibik ◽  
Fikriye Yilmaz
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Error Bounds ◽  
A Priori ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
A Priori Error Bounds ◽  
Variational Form ◽  
The Stability

In this study, we consider a Brezzi-Pitkaranta stabilization scheme for the optimal control problem governed by stationary Stokes equation, using a P1-P1 interpolation for velocity and pressure. We express the stabilization as extra terms added to the discrete variational form of the problem.  We first prove the stability of the finite element discretization of the problem. Then, we derive a priori error bounds for each variable and present a numerical example to show the effectiveness of the stabilization clearly.

Sign in / Sign up

Export Citation Format

Share Document