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A Nonconforming Nitsche’s Extended Finite Element Method for Stokes Interface Problems

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Abstract

This article studies the nonconforming \(P_{1}/P_{0}\) Nitsche’s extended finite element method for Stokes interface problems with interface-unfitted meshes. We derive the inf-sup stability result and optimal a priori error estimates in spite of the low regularity of interface problems. It is shown that all results are independent of not only the viscosity parameters but also the position of the interface without other assumption for the interface. Numerical experiments are carried out to validate theoretical results.

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Acknowledgements

The authors would like to thank reviewers for their comments and suggestions, which are valuable in improving the quality of the manuscript.

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  1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Nan Wang & Jinru Chen

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  1. Nan Wang
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  2. Jinru Chen
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Correspondence to Jinru Chen.

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This work was supported by the NSFC Grants 11871281 and 11731007.

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Wang, N., Chen, J. A Nonconforming Nitsche’s Extended Finite Element Method for Stokes Interface Problems. J Sci Comput 81, 342–374 (2019). https://doi.org/10.1007/s10915-019-01019-9

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  • DOI: https://doi.org/10.1007/s10915-019-01019-9

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