A two level finite element method for Stokes constrained Dirichlet boundary control problem

In this paper we present a finite element analysis for Dirichlet boundary control problem governed by the Stokes equation. The is considered in convex closed subset of energy space H1(Ω). Most previous works on deals with either tangential or case where flux zero. This choice very particular and their formulation leads to limited regularity. To overcome difficulty, introduce outflow condition acts only hence our more general it has both normal components. We prove well-posedness discuss regularity problem. first-order optimality Signorini develop two-level discretization using P1 elements (on fine mesh) velocity variable P0 coarse pressure variable. standard error gives 12+δ2 order convergence when H32+δ(Ω) space. Here have improved 12+δ, which optimal. Also, lies less regular derived optimal up theoretical results are corroborated variety numerical tests.