Adaptive Regularisation for PDE-Constrained Optimal Control

2025/03/14 by Jenny Power, Power, Jenny, Tristan Pryer +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2503.11386

openalex publication_date 2025/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both regularisation and discretisation adaptivity, varying both the regularisation parameter and mesh-size locally based on rigorous a posteriori error estimates aiming to dynamically balance induced regularisation and discretisation errors, offering a robust and efficient method for solving these problems. We demonstrate the efficacy of our analysis with several numerical experiments.

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• State-based nested iteration solution of optimal control problems with PDE constraints

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