English

A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization

Optimization and Control 2025-06-13 v1 Numerical Analysis Numerical Analysis

Abstract

This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and adjoint. This problem is shown to be equivalent to our optimal control problem. Based on fully unstructured, space-time interface-fitted meshes, we propose and analyze a Petrov-Galerkin approximation of the problem. An optimal error estimate with respect to a discrete norm is established under a specific regularity assumption on the state and adjoint. Several numerical results are presented to corroborate our theoretical results.

Keywords

Cite

@article{arxiv.2506.10924,
  title  = {A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization},
  author = {Quang Huy Nguyen and Phuong Cuc Hoang and Van Chien Le and Thi Thanh Mai Ta},
  journal= {arXiv preprint arXiv:2506.10924},
  year   = {2025}
}
R2 v1 2026-07-01T03:13:56.922Z