Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization
作者：
Highlights：
• The presented paper contributies to the numerical approximation of optimal controls problems of NSE.
• It includes the fully discrete optimal control problem of NSE with curvature based stabilization.
• Since the non-linear terms are treated through a second order extrapolation one solves only linear systems of equations at each time step which makes the scheme faster and less memory consuming.
• We propose an IMEX-time stepping scheme for the adjoint equation by reversing the time.
• A priori error analysis is obtained for both the state and adjoint state equations.
• Numerical experiments shows the efficiency of the proposed scheme and verify the theory.
摘要
•The presented paper contributies to the numerical approximation of optimal controls problems of NSE.•It includes the fully discrete optimal control problem of NSE with curvature based stabilization.•Since the non-linear terms are treated through a second order extrapolation one solves only linear systems of equations at each time step which makes the scheme faster and less memory consuming.•We propose an IMEX-time stepping scheme for the adjoint equation by reversing the time.•A priori error analysis is obtained for both the state and adjoint state equations.•Numerical experiments shows the efficiency of the proposed scheme and verify the theory.
论文关键词：Finite element method,Navier-Stokes equations,Optimal control,Curvature stabilization
论文评审过程：Received 18 January 2022, Revised 15 April 2022, Accepted 7 May 2022, Available online 23 May 2022, Version of Record 23 May 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127240
