@Article{AAMM-10-634,
author = {He , Qiaolin and Lv , Xiaomin},
title = {A New Fictitious Domain Method for Elliptic Problems with the Third Type Boundary Conditions},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {3},
pages = {634--651},
abstract = {<p style="text-align: justify;">In this article, we discuss a modified least–squares fictitious domain method for the solution of linear elliptic boundary value problems with the third type of boundary conditions (Robin boundary conditions). Let $\Omega$ and $\omega$ be two bounded domains of $\mathbb{R}^{d}$ such that &nbsp;$\overline{\omega} \subset \Omega$. &nbsp;For a linear elliptic problem in $\Omega\setminus \overline{\omega}$ with Robin boundary conditions on the boundary $\gamma$ of $\omega$, we accelerate the original least–squares fictitious domain method in Glowinski &amp; He [1] and present a modified least–squares formulation. This method is still a virtual control type and relies on a least-squares formulation, which makes the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Numerical results show that our method costs much less iterations and the optimal order of convergence is obtained.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2017-0193},
url = {http://global-sci.org/intro/article_detail/aamm/12228.html}
}