- Journal Home
- Volume 22 - 2025
- Volume 21 - 2024
- Volume 20 - 2023
- Volume 19 - 2022
- Volume 18 - 2021
- Volume 17 - 2020
- Volume 16 - 2019
- Volume 15 - 2018
- Volume 14 - 2017
- Volume 13 - 2016
- Volume 12 - 2015
- Volume 11 - 2014
- Volume 10 - 2013
- Volume 9 - 2012
- Volume 8 - 2011
- Volume 7 - 2010
- Volume 6 - 2009
- Volume 5 - 2008
- Volume 4 - 2007
- Volume 3 - 2006
- Volume 2 - 2005
- Volume 1 - 2004
Int. J. Numer. Anal. Mod., 22 (2025), pp. 694-727.
Published online: 2025-05
Cited by
- BibTex
- RIS
- TXT
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface with a diffuse layer of thickness $ε,$ which scales with the minimum grid size. This approach reformulates the original equations on an extended regular domain, incorporating boundary conditions through singular source terms. In this work, we conduct a matched asymptotic analysis of a DDM for a two-sided problem with transmission-type Robin boundary conditions. Our results show that, in the one dimensional space, the solution of the diffuse domain approximation asymptotically converges to the solution of the original problem, with exactly first-order accuracy in $ε.$ Furthermore, we provide numerical simulations that validate and illustrate the analytical result.
}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1030}, url = {http://global-sci.org/intro/article_detail/ijnam/24082.html} }Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface with a diffuse layer of thickness $ε,$ which scales with the minimum grid size. This approach reformulates the original equations on an extended regular domain, incorporating boundary conditions through singular source terms. In this work, we conduct a matched asymptotic analysis of a DDM for a two-sided problem with transmission-type Robin boundary conditions. Our results show that, in the one dimensional space, the solution of the diffuse domain approximation asymptotically converges to the solution of the original problem, with exactly first-order accuracy in $ε.$ Furthermore, we provide numerical simulations that validate and illustrate the analytical result.