Abstract
This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with \(H^1\) initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank–Nicolson scheme, with the usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.
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Funding
The research of Buyang Li and Shu Ma were partially funded by the internal grant ZZKQ at The Hong Kong Polytechnic University. The research of Na Wang was partially funded by the National Natural Science Foundation of China (NSFC Grant U1930402).
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Li, B., Ma, S. & Wang, N. Second-Order Convergence of the Linearly Extrapolated Crank–Nicolson Method for the Navier–Stokes Equations with \(\mathbf{H^1}\) Initial Data. J Sci Comput 88, 70 (2021). https://doi.org/10.1007/s10915-021-01588-8
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DOI: https://doi.org/10.1007/s10915-021-01588-8
Keywords
- Navier–Stokes equations
- Linearly extrapolated Crank–Nicolson method
- Locally refined stepsizes
- Nonsmooth initial data
- Error estimate