@Article{CiCP-9-587,
author = {},
title = {A Least-Squares/Fictitious Domain Method for Linear Elliptic Problems with Robin Boundary Conditions},
journal = {Communications in Computational Physics},
year = {2011},
volume = {9},
number = {3},
pages = {587--606},
abstract = {<p style="text-align: justify;">In this article, we discuss a least-squares/fictitious domain method for the
solution of linear elliptic boundary value problems with Robin boundary conditions.
Let Ω and ω be two bounded domains of <strong>R</strong><sup>d&nbsp;</sup>such that ω⊂Ω. For a linear elliptic problem
in Ω\ω with Robin boundary condition on the boundary γ of ω, our goal here is to
develop a fictitious domain method where one solves a variant of the original problem
on the full Ω, followed by a well-chosen correction over ω. This method is of the virtual
control type and relies on a least-squares formulation making the problem solvable by
a conjugate gradient algorithm operating in a well chosen control space. Numerical results
obtained when applying our method to the solution of two-dimensional elliptic
and parabolic problems are given; they suggest optimal order of convergence.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.071009.160310s},
url = {http://global-sci.org/intro/article_detail/cicp/7512.html}
}