A Least-Squares/Fictitious Domain Method for Linear Elliptic Problems with Robin Boundary Conditions
Year: 2011
Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 587–606
Abstract
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 Rd 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.071009.160310s
Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 587–606
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
-
An inverse problem formulation of the immersed‐boundary method
Yan, Jianfeng | Hicken, Jason E.International Journal for Numerical Methods in Fluids, Vol. 92 (2020), Iss. 9 P.1037
https://doi.org/10.1002/fld.4816 [Citations: 1] -
A least-squares/fictitious domain method for incompressible viscous flow around obstacles with Navier slip boundary condition
He, Qiaolin | Glowinski, Roland | Wang, Xiao-PingJournal of Computational Physics, Vol. 366 (2018), Iss. P.281
https://doi.org/10.1016/j.jcp.2018.04.013 [Citations: 5] -
FDM-PINN: Physics-informed neural network based on fictitious domain method
Yang, Qihong | Yang, Yu | Cui, Tao | He, QiaolinInternational Journal of Computer Mathematics, Vol. 100 (2023), Iss. 3 P.511
https://doi.org/10.1080/00207160.2022.2128674 [Citations: 1] -
The least–square/fictitious domain method based on Navier slip boundary condition for simulation of flow–particle interaction
Zhang, Rong | He, QiaolinApplied Mathematics and Computation, Vol. 415 (2022), Iss. P.126687
https://doi.org/10.1016/j.amc.2021.126687 [Citations: 1] -
Investigations on boundary temperature control analysis considering a moving body based on the adjoint variable and the fictitious domain finite element methods
Kurahashi, T.
International Journal for Numerical Methods in Engineering, Vol. 103 (2015), Iss. 8 P.582
https://doi.org/10.1002/nme.4908 [Citations: 4] -
The Smooth Extension Embedding Method
Agress, Daniel J. | Guidotti, Patrick Q.SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 1 P.A446
https://doi.org/10.1137/19M1300844 [Citations: 4]