Work

Adaptive regularisation for PDE-constrained optimal control

Year: 2025

Type: article

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.

Source: Journal of Computational and Applied Mathematics

DOI: 10.1016/j.cam.2025.116651

Authors: Jenny Power, Tristan Pryer

Institution: University of Bath

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: Leverhulme Trust, Engineering and Physical Sciences Research Council