2018/02/08 by Niklas Behringer, Behringer, Niklas, Dominik Meidner +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1802.02918
openalex publication_date 2018/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three different approaches are considered. The main goal of the paper is to significantly improve known a priori discretization error estimates for this problem. We prove optimal error estimates for cellwise constant control discretizations in two and three space dimensions. Further, in two space dimensions, optimal error estimates for variational discretization and for the post-processing approach are derived.