Subgrid scale eddy viscosity finite element method on optimal control of system governed by unsteady Oseen equations

In this paper we focus on numerical analysis of finite element methods with stabilizations for the optimal control of system governed by unsteady Oseen equations. Using continuous equal-order finite elements for both velocities and pressure, two fully discrete schemes are proposed. Convective effects and pressure are stabilized by adding a subgrid scale eddy viscosity term and a pressure stabilized term. Convergence of the approximate solution is proved. A-Priori error estimates are obtained uniformly with Reynolds number, especially the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$L^2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> </EquationSource> </InlineEquation>-error estimates of numerical solution are independent of Reynolds number. The numerical experiments are shown to be consistent with our theoretical analysis. Copyright Springer Science+Business Media New York 2014