Adaptive finite element methods for the pointwise tracking optimal control problem of the Stokes equations

摘要: We propose and analyze a reliable efficient posteriori error estimator for the pointwise tracking optimal control problem of Stokes equations. This linear-quadratic entails minimization cost functional that involves point evaluations velocity field solves state leads to an adjoint with linear combination Dirac measures as forcing term whose solution exhibits reduced regularity properties. also consider constraints on variable. The proposed can be decomposed sum four contributions: three contributions related discretization equations, another contribution accounts On basis devised estimator, we design simple adaptive strategy illustrates our theory competitive performance.