@Article{IJNAM-22-5,
author = {Toai, Luong and Tadele, Mengesha and Wise, Steven, M. and Wong, Ming, Hei},
title = {A Diffuse Domain Approximation with Transmission-Type Boundary Conditions II: Gamma-Convergence },
journal = {International Journal of Numerical Analysis and Modeling},
year = {2025},
volume = {22},
number = {5},
pages = {728--744},
abstract = {<p style="text-align: justify;">Diffuse domain methods (DDMs) have gained significant attention for solving partial
differential equations (PDEs) on complex geometries. These methods approximate the domain
by replacing sharp boundaries with a diffuse layer of thickness $ε,$ which scales with the minimum
grid size. This reformulation extends the problem to a regular domain, incorporating boundary conditions via singular source terms. In this work, we analyze the convergence of a DDM
approximation problem with transmission-type Neumann boundary conditions. We prove that
the energy functional of the diffuse domain problem $Γ$-converges to the energy functional of the
original problem as $ε → 0.$ Additionally, we show that the solution of the diffuse domain problem
strongly converges in $H^1
(Ω),$ up to a subsequence, to the solution of the original problem, as $ε → 0.$</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2025-1031},
url = {https://global-sci.com/article/91879/a-diffuse-domain-approximation-with-transmission-type-boundary-conditions-ii-gamma-convergence}
}