Baek, Hunki; Kim, Sang Dong; Lee, Hyung-Chun A multigrid method for an optimal control problem of a diffusion-convection equation. (English) Zbl 1179.49027 J. Korean Math. Soc. 47, No. 1, 83-100 (2010). Summary: An optimal control problem associated with convection-diffusion equation is considered. Using Lagrange multiplier, the optimality system is obtained. The derived optimal system turns to coupled, non-symmetric partial differential equations. For discretization and implementations, the finite element multigrid \(V\)-cycle is employed. The convergence analysis of finite element multigrid methods for the derived optimal system is shown. Some numerical simulations are performed. Cited in 1 Document MSC: 49K20 Optimality conditions for problems involving partial differential equations 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 49M25 Discrete approximations in optimal control Keywords:optimal control problem; multigrid method; diffusion-convection equation PDFBibTeX XMLCite \textit{H. Baek} et al., J. Korean Math. Soc. 47, No. 1, 83--100 (2010; Zbl 1179.49027) Full Text: DOI