An error estimator for spectral method approximation of flow control with state constraint

Abstract

We consider the spectral approximation of flow optimal control problems with state constraint. The main contribution of this work is to derive an a posteriori error estimator, and show the upper and lower bounds for the approximation error. Numerical experiment shows the efficiency of the error indicator, which will be used to construct reliable adaptive hp spectral element approximation for flow control in the future work.

Keywords

• spectral method
• optimal control
• state constraint
• stokes equations
• upper and lower bounds