A New Error Analysis for Finite Element Methods for Elliptic Neumann Boundary Control Problems with Pointwise Control Constraints

2024/11/03 by Susanne C. Brenner, Brenner, Susanne C., Li-Yeng Sung +1 · 1 citation
Computer Science · Engineering · Mathematics · #49M41 #65K10 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2411.01550

openalex publication_date 2024/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when the coefficient s in the elliptic operator are smooth and also to multiscale finite element methods when the coefficients are rough.

Cited by

• State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation

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