2018/10/04 by Alejandro Allendes, Francisco Fuica, Allendes, Alejandro +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in inverse problems #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1810.02415
openalex publication_date 2018/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose and analyze a reliable and efficient a posteriori error estimator\nfor the pointwise tracking optimal control problem of the Stokes equations.\nThis linear-quadratic optimal control problem entails the minimization of a\ncost functional that involves point evaluations of the velocity field that\nsolves the state equations. This leads to an adjoint problem with a linear\ncombination of Dirac measures as a forcing term and whose solution exhibits\nreduced regularity properties. We also consider constraints on the control\nvariable. The proposed a posteriori error estimator can be decomposed as the\nsum of four contributions: three contributions related to the discretization of\nthe state and adjoint equations, and another contribution that accounts for the\ndiscretization of the control variable. On the basis of the devised a\nposteriori error estimator, we design a simple adaptive strategy that\nillustrates our theory and exhibits a competitive performance.\n