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arXiv · 2510.27336

Numerical solution of elliptic distributed optimal control problems with boundary value tracking

Ulrich Langer·Richard Löscher·Olaf Steinbach·Huidong Yang
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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.

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Ulrich Langer, Richard Löscher, Olaf Steinbach, Huidong Yang. 2025-10-31. Numerical solution of elliptic distributed optimal control problems with boundary value tracking. https://arxiv.org/abs/2510.27336

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