Numerical solution of elliptic distributed optimal control problems with boundary value tracking
Numerical Analysis
2026-03-12 v2 Numerical Analysis
Optimization and Control
Abstract
We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be reformulated asa state-based variational problem that is the starting point for the finite element discretizion. In this paper, we only consider atensor-product finite element discretizion for which optimal discretization error estimates and fast solvers can be derived.Numerical experiments illustrate the theoretical results quantitatively.
Cite
@article{arxiv.2510.27336,
title = {Numerical solution of elliptic distributed optimal control problems with boundary value tracking},
author = {Ulrich Langer and Richard Löscher and Olaf Steinbach and Huidong Yang},
journal= {arXiv preprint arXiv:2510.27336},
year = {2026}
}