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Euler implicit/explicit iterative scheme for the stationary Navier–Stokes equations

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Abstract

In this paper, a new uniqueness assumption (A2) of the solution for the stationary Navier–Stokes equations is presented. Under assumption (A2), the exponential stability of the solution \((\bar{u},\bar{p})\) for the stationary Navier–Stokes equations is proven. Moreover, the Euler implicit/explicit scheme based on the mixed finite element is applied to solve the stationary Navier–Stokes equations. Finally, the almost unconditionally stability is proven and the optimal error estimates uniform in time are provided for the scheme.

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Acknowledgments

We would like to thank the editor and reviewers for their criticism, valuable comments, and suggestions which helped to improve the results of this paper.

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Correspondence to Yinnian He.

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This research was subsidized by the NSF of China (No. 10971166).

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He, Y. Euler implicit/explicit iterative scheme for the stationary Navier–Stokes equations. Numer. Math. 123, 67–96 (2013). https://doi.org/10.1007/s00211-012-0482-8

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  • DOI: https://doi.org/10.1007/s00211-012-0482-8

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