| Issue |
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 3069 - 3105 | |
| DOI | https://doi.org/10.1051/m2an/2025084 | |
| Published online | 17 November 2025 | |
Asymptotic compatibility of parametrized optimal design problems
1
Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
2
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
* Corresponding author: asalgad1@utk.edu
Received:
20
January
2025
Accepted:
30
September
2025
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit of this (modeling) parameter. We develop a framework that guarantees asymptotic compatibility, that is unconditional convergence with respect to modeling and discretization parameters to the solution of the corresponding limiting problems. This framework is then applied to two distinct classes of problems where the modeling parameter represents the degree of nonlocality. Specifically, we show unconditional convergence of optimal design problems when the state equation is either a scalar-valued fractional equation, or a strongly coupled system of nonlocal equations derived from the bond-based model of peridynamics.
Mathematics Subject Classification: 49M41 / 49M25 / 45F15 / 65R20 / 74P05
Key words: Optimal design / asymptotic compatibility / finite element method / varying fractional parameter
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.