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arXiv · 2407.08439

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

Quang Huy Nguyen·Van Chien Le·Phuong Cuc Hoang·Thi Thanh Mai Ta
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Abstract

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.

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Quang Huy Nguyen, Van Chien Le, Phuong Cuc Hoang, Thi Thanh Mai Ta. 2024-07-11. A fitted space-time finite element method for an advection-diffusion problem with moving interfaces. https://doi.org/10.1016/j.apnum.2025.01.002

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