Variational Discretization for Optimal Control Governed by Convection Dominated Diffusion Equations (Journal of Computational Mathematics, 2018)
In this paper, we study variational discretization for the constrained optimal controlproblem governed by convection dominated diffusion equations, where the state equationis approximated by the edge stabilization Galerkin method. A priori error estimates arederived for the state, the adjoint state and the control. Moreover, residual type a posteriorierror estimates in the $L^2$-norm are obtained. Finally, two numerical experiments arepresented to illustrate the theoretical results.
Keywords: Constrained optimal control problem; Convection dominated diffusion equation; Edge stabilization Galerkin method; Variational discretization; A priori error estimate; A posteriori error estimate.