TY - JOUR T1 - Variational Discretization for Optimal Control Governed by Convection Dominated Diffusion Equations JO - Journal of Computational Mathematics VL - 2-3 SP - 237 EP - 253 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8570.html KW - Constrained optimal control problem, Convection dominated diffusion equation, Edge stabilization Galerkin method, Variational discretization, A priori error estimate, A posteriori error estimate. AB -

In this paper, we study variational discretization for the constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization Galerkin method. A priori error estimates are derived for the state, the adjoint state and the control. Moreover, residual type a posteriori error estimates in the $L^2$-norm are obtained. Finally, two numerical experiments are presented to illustrate the theoretical results.