Adaptive regularisation for PDE constrained optimal control

Jenny Power; Tristan Pryer

doi:10.1016/j.cam.2025.116651

Adaptive regularisation for PDE constrained optimal control

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	116651
Journal	Journal of Computational and Applied Mathematics
Volume	470
Early online date	28 Mar 2025
DOIs	https://doi.org/10.1016/j.cam.2025.116651
Publication status	E-pub ahead of print - 28 Mar 2025

Data Availability Statement

Data will be made available on request.

Funding

JP is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/S022945/1. TP received support from the EPSRC programme grant EP/W026899/1 and was also supported by the Leverhulme RPG-2021-238 and EPSRC grant EP/X030067/1.

Funders	Funder number
EPSRC Centre for Doctoral Training in Statistical	EP/S022945/1
Engineering and Physical Sciences Research Council	EP/W026899/1
Leverhulme Trust	EP/X030067/1, RPG-2021-238

Keywords

A posteriori error estimates
Adaptive regularisation
Finite element methods
PDE-constrained optimal control

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.cam.2025.116651Licence: CC BY

Cite this

@article{2cefd6c1ab794fc1a28cefb80bfd106e,

title = "Adaptive regularisation for PDE constrained optimal control",

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.",

keywords = "A posteriori error estimates, Adaptive regularisation, Finite element methods, PDE-constrained optimal control",

author = "Jenny Power and Tristan Pryer",

year = "2025",

month = mar,

day = "28",

doi = "10.1016/j.cam.2025.116651",

language = "English",

volume = "470",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Adaptive regularisation for PDE constrained optimal control

AU - Power, Jenny

AU - Pryer, Tristan

PY - 2025/3/28

Y1 - 2025/3/28

N2 - 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.

AB - 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.

KW - A posteriori error estimates

KW - Adaptive regularisation

KW - Finite element methods

KW - PDE-constrained optimal control

UR - http://www.scopus.com/inward/record.url?scp=105002485779&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2025.116651

DO - 10.1016/j.cam.2025.116651

M3 - Article

SN - 0377-0427

VL - 470

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 116651

ER -

Adaptive regularisation for PDE constrained optimal control

Abstract

Data Availability Statement

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this