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

2025/10/31 by Ulrich Langer, Richard Löscher, Langer, Ulrich +5
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2510.27336

openalex publication_date 2025/10/31 · openalex created_date 2025/11/05 · openalex updated_date 2026/07/28

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.

Citations

• Sharp Boundary Trace Theory and Schrödinger Operators on Bounded Lipschitz Domains
• Robust preconditioning and error estimates for optimal control of the convection-diffusion-reaction equation with limited observation in Isogeometric analysis
• Robust preconditioners for PDE-constrained optimization with limited\n observations

Related

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• Numerical analysis of distributed optimal control problems governed by\n elliptic variational inequalities
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