2016/05/12 by Alejandro Allendes, Enrique Otárola, Allendes, Alejandro +5 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1605.04027
openalex publication_date 2016/05/12 · openalex created_date 2022/10/03 · openalex updated_date 2026/08/01
The purpose of this work is the design and analysis of a reliable and\nefficient a posteriori error estimator for the so-called pointwise tracking\noptimal control problem. This linear-quadratic optimal control problem entails\nthe minimization of a cost functional that involves point evaluations of the\nstate, thus leading to an adjoint problem with Dirac measures on the right hand\nside; control constraints are also considered. The proposed error estimator\nrelies on a posteriori error estimates in the maximum norm for the state and in\nMuckenhoupt weighted Sobolev spaces for the adjoint state. We present an\nanalysis that is valid for two and three-dimensional domains. We conclude by\npresenting several numerical experiments which reveal the competitive\nperformance of adaptive methods based on the devised error estimator.\n