The fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition

We consider the fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition. For the penalty method, we obtain the error estimate of order O ( ϵ ) , where ϵ is the penalty parameter. Next, we apply the finite element method to the penalty problem using the P1/P1 ele...

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Bibliographic Details
Published in:	Japan journal of industrial and applied mathematics Vol. 34; no. 2; pp. 585 - 610
Main Author:	Zhou, Guanyu
Format:	Journal Article
Language:	English
Published:	Tokyo Springer Japan 01.08.2017
Subjects:	Applications of Mathematics Computational Mathematics and Numerical Analysis Mathematics Mathematics and Statistics Original Paper Finite element method Stokes problem Error estimate Fictitious domain method Primary 65N85 Penalty method 65N30 34M40
ISSN:	0916-7005, 1868-937X
Online Access:	Get full text
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Summary:	We consider the fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition. For the penalty method, we obtain the error estimate of order O ( ϵ ) , where ϵ is the penalty parameter. Next, we apply the finite element method to the penalty problem using the P1/P1 element with stabilization, and obtain the error estimate of discretization. The theoretical results are verified by the numerical experiments.
ISSN:	0916-7005 1868-937X
DOI:	10.1007/s13160-017-0255-y