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

Aytekin Çıbık | Zendy; Fikriye Yılmaz | Zendy

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

Author(s) -

Aytekin Çıbık,

Fikriye Yılmaz

Publication year - 2016

Publication title -

an international journal of optimization and control theories and applications (ijocta)

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.287

H-Index - 6

eISSN - 2146-5703

pISSN - 2146-0957

DOI - 10.11121/ijocta.01.2017.00312

Subject(s) - discretization , a priori and a posteriori , interpolation (computer graphics) , stokes problem , mathematics , stability (learning theory) , finite element method , variable (mathematics) , mathematical analysis , element (criminal law) , error analysis , computer science , physics , classical mechanics , motion (physics) , philosophy , epistemology , machine learning , political science , law , thermodynamics

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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