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

• Main Authors: Aytekin Cibik, Fikriye Yilmaz
• Format: Article
• Language: English
• Published: Balikesir University 2016-12-01
• Series: An International Journal of Optimization and Control: Theories & Applications
• Subjects: Finite element; Brezzi-Pitkaranta stabilization; optimal control; Stokes equations
• Online Access: http://ijocta.balikesir.edu.tr/index.php/files/article/view/312

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.