arXiv subjects

Phuong Cuc Hoang

Publications and source records attributed to Phuong Cuc Hoang.

2 recordsLinked to original sources

arXiv2025

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

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.

math.OC↗

arXiv2025

A fitted space-time finite element method for an advection-diffusion problem with moving interfaces

This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution gradient across the interface. We use the Banach-Necas-Babuska theorem to show the well-posedness of the continuous variational problem. A fully discrete finite-element based scheme is analyzed using the Galerkin method and unstructured interface-fitted meshes. An optimal error estimate is established in a discrete energy norm under a globally low but locally high regularity condition. Some numerical results corroborate our theoretical results.

math.NA↗