2019/07/25 by Francisco Fuica, Fuica, Francisco, Enrique Otárola +3
Engineering · #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1907.11096
openalex publication_date 2019/07/25 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
The aim of this work is to derive a priori error estimates for finite element\ndiscretizations of control--constrained optimal control problems that involve\nthe Stokes system and Dirac measures. The first problem entails the\nminimization of a cost functional that involves point evaluations of the\nvelocity field that solves the state equations. This leads to an adjoint\nproblem with a linear combination of Dirac measures as a forcing term and whose\nsolution exhibits reduced regularity properties. The second problem involves a\ncontrol variable that corresponds to the amplitude of forces modeled as point\nsources. This leads to a solution of the state equations with reduced\nregularity properties. For each problem, we propose a finite element solution\ntechnique and derive a priori error estimates. Finally, we present numerical\nexperiments, in two and three dimensions, that illustrate our theoretical\ndevelopments.\n