In this paper,spectral approximations for distributed optimal control problems governed by the Stokes equation are considered.And the constraint set on velocity is stated with L2-norm.Optimality conditions of the cont...In this paper,spectral approximations for distributed optimal control problems governed by the Stokes equation are considered.And the constraint set on velocity is stated with L2-norm.Optimality conditions of the continuous and discretized systems are deduced with the Karush-Kuhn-Tucker conditions and a Lagrange multiplier depending on the constraint.To solve the equivalent systems with high accuracy,Galerkin spectral approximations are employed to discretize the constrained optimal control systems.Meanwhile,we adopt a parameter l in the pressure approximation space,which also guarantees the inf-sup condition,and study a priori error estimates for the velocity and pressure.Specially,an efficient algorithm based on the Uzawa algorithm is proposed and its convergence results are investigated with rigorous analyses.Numerical experiments are performed to confirm the theoretical results.展开更多
基金supported by NSFC grants(Nos.11926355,and 11701253)NSF of Henan Province(No.15A110024)+1 种基金NSF of Shandong Province(Nos.ZR2019YQ05,2019KJI003,and 2017GSF216001)China Postdoctoral Science Foundation(Nos.2017T100030,and 2017M610751)。
文摘In this paper,spectral approximations for distributed optimal control problems governed by the Stokes equation are considered.And the constraint set on velocity is stated with L2-norm.Optimality conditions of the continuous and discretized systems are deduced with the Karush-Kuhn-Tucker conditions and a Lagrange multiplier depending on the constraint.To solve the equivalent systems with high accuracy,Galerkin spectral approximations are employed to discretize the constrained optimal control systems.Meanwhile,we adopt a parameter l in the pressure approximation space,which also guarantees the inf-sup condition,and study a priori error estimates for the velocity and pressure.Specially,an efficient algorithm based on the Uzawa algorithm is proposed and its convergence results are investigated with rigorous analyses.Numerical experiments are performed to confirm the theoretical results.
