Adaptive Regularisation for PDE-Constrained Optimal Control

Jenny Power; Tristan Pryer

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arXiv · 2503.11386

Adaptive Regularisation for PDE-Constrained Optimal Control

Jenny Power·Tristan Pryer

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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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Jenny Power, Tristan Pryer. 2025-03-14. Adaptive Regularisation for PDE-Constrained Optimal Control. https://arxiv.org/abs/2503.11386

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