Analysis and Approximations of Dirichlet Boundary Control of Stokes Flows in the Energy Space

We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. consider cost functionals with two different regularization terms: the $L^2$ norm and an energy space seminorm. prove well-posedness regularity results for both problems, develop finite element discretizations error estimates latter problem. The motivation to problem follows from our analysis: we that choice ${\bm L}^2(\Gamma)$ can lead optimal discontinuities at corners, even when domain is convex. observe this phenomenon numerical experiments. This behavior does not occur problems Poisson equation on convex domains, may be desirable real applications. For problem, derive first order optimality conditions, show solution more regular than regularization. also a priori norm, present several experiments nonconvex