TY  - JOUR
T1  - Stabilized Finite Element Solution of Control Problem of Convection Diffusion Equation
AU  - Yılmaz, Fikriye Nuray
PY  - 2018
DA  - December
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 281
EP  - 284
IS  - 4
LA  - en
AB  - Inthis work, we consider the stabilized numerical solutions of optimal controlproblems of convection diffusion equation of this type of equations have beencommonly studied in the literature. We use finite element method (FEM). Becauseof the viscosity term in the problem, the FEM solution blows up if Reynoldnumber is large. In this case, the solution is unstabilized so that astabilization technique is needed. As for stabilization technique, we applyboth variational multiscale (VMS) and grad-div stabilization technique. Thevariational multiscale method is reviewed as a framework for developingcomputational methods for large-eddy simulation of turbulent flow. Some of themost used numerical stabilization techniques for flow problems are streamlineupwind Galerkin (SUPG) and pressure stabilization methods, large eddysimulation (LES) methods, and VMS methods. First of all, we obtain theoptimality system. We then use FEM to obtain the discrete system. We obtain thetheoretical stability results. We use the package freefem ++ to get thenumerical results. We compare the stabilized solutions.
KW  - Optimal control
KW  - Convection-diffusion equation
KW  - Stabilized fem
CR  - Abergel F. and Temam R.(1990), On some optimal control problems in fluidmechanics, Theoret. Comput. Fluid Mech. 1 (6) 303-325.
Hecht F.(2012), New development in FreeFem++, J. Numer. Math. 20, no. 3-4, 251-265.
John V., Kaya S. and Layton W.(2005), A two-level variational multiscale methodfor convection-diffusion equations, Comput. Meth. Appl. Mech. Engrg., 195, 4594-4603, 2005.
UR  - https://dergipark.org.tr/en/pub/epstem/issue//498146
L1  - https://dergipark.org.tr/en/download/article-file/598410
ER  -