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A Viscosity-Independent Error Estimate of a Pressure-Stabilized Lagrange–Galerkin Scheme for the Oseen Problem

  • Shinya UchiumiEmail author
Article
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Abstract

We consider a pressure-stabilized Lagrange–Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order k for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the velocity with a constant independent of the viscosity if the exact solution is sufficiently smooth. We also show an error estimate of a discrete primitive of the pressure. Numerical examples show high accuracy of the scheme for problems with small viscosity.

Keywords

Transient Oseen problem Lagrange–Galerkin scheme Finite element method Equal-order elements Symmetric pressure stabilization Dependence on viscosity 

Mathematics Subject Classification

65M12 65M25 65M60 76D07 76M10 

Notes

Acknowledgements

The author is thankful to anonymous reviewers for their valuable comments that improve this paper. The author would like to express his gratitude to Professor Emeritus Masahisa Tabata of Kyushu University for valuable discussions and encouragements. This work was supported by Japan Society for the Promotion of Science (JSPS) under Grant-in-Aid for JSPS Fellows, No. 26\(\cdot \)964, and under the Japanese-German Graduate Externship (Mathematical Fluid Dynamics), and by CREST, Japan Science and Technology Agency.

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Copyright information

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Authors and Affiliations

  1. 1.Department of Applied MathematicsWaseda UniversityTokyoJapan
  2. 2.Department of MathematicsGakushuin UniversityTokyoJapan

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