Optimal Control of the Stokes Equations: A Priori Error Analysis for Finite Element Discretization with Postprocessing

2006 ◽  
Vol 44 (5) ◽  
pp. 1903-1920 ◽  
Author(s):  
Arnd Rösch ◽  
Boris Vexler
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Analysis ◽  
Stokes Equations ◽  
A Priori ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
A Priori Error Analysis

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.

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