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A multigrid method for an optimal control problem of a diffusion-convection equation. (English) Zbl 1179.49027

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.

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
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