Year: 2018
Author: Qiaolin He, Xiaomin Lv
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 3 : pp. 634–651
Abstract
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 $\overline{\omega} \subset \Omega$. 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 & 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2017-0193
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 3 : pp. 634–651
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Least–squares methods fictitious domain methods finite element methods Robin boundary conditions.
Author Details
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