Variational discretization for optimal control governed by convection dominated diffusion equations. (English) Zbl 1212.65248
Summary: We study the variational discretization for a 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.
MSC:
65K10 | Numerical optimization and variational techniques |
49J20 | Existence theories for optimal control problems involving partial differential equations |
49M30 | Other numerical methods in calculus of variations (MSC2010) |