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

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Abstract

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 \(O(\epsilon )\), where \(\epsilon \) 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.

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Acknowledgements

I would like to express my gratitude to N. Saito who brought my attention to the present subject and encouraged me through valuable discussions. A part of this work is supported by Core Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Agency (JST), Japan, and by Platform for Dynamic Approaches to Living System from the Ministry of Education, Culture, Sports, Science and Technology, Japan. This work was also supported by JSPS A3 Foresight Program.

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  1. Department of Applied Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Guanyu Zhou

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  1. Guanyu Zhou
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Zhou, G. The fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition. Japan J. Indust. Appl. Math. 34, 585–610 (2017). https://doi.org/10.1007/s13160-017-0255-y

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  • DOI: https://doi.org/10.1007/s13160-017-0255-y

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