A new linearly extrapolated Crank-Nicolson time-stepping scheme for the Navier-Stokes equations
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Abstract:
We investigate the stability of a fully-implicit, linearly extrapolated Crank-Nicolson (CNLE) time-stepping scheme for finite element spatial discretization of the Navier-Stokes equations. Although presented in 1976 by Baker and applied and analyzed in various contexts since then, all known convergence estimates of CNLE require a time-step restriction. We propose a new linear extrapolation of the convecting velocity for CNLE that ensures energetic stability without introducing an undesirable exponential Gronwall constant. Such a result is unknown for conventional CNLE for inhomogeneous boundary data (usual techniques fail!). Numerical illustrations are provided showing that our new extrapolation clearly improves upon stability and accuracy from conventional CNLE.References
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Additional Information
- Ross Ingram
- Affiliation: University of Pittsburgh, 615 Thackeray Hall, Pittsburgh Pennsylvania 15260
- Address at time of publication: 2259 Shady Avenue, Pittsburgh, Pennsylvania 15217
- Email: rni1@psualum.com
- Received by editor(s): June 14, 2011
- Received by editor(s) in revised form: January 8, 2012
- Published electronically: March 20, 2013
- Additional Notes: The author was partially supported by NSF Grants DMS 0508260 and 080385
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 82 (2013), 1953-1973
- MSC (2010): Primary 65M12, 65M60, 76D05, 76M10, 76M20; Secondary 76D15, 76M25, 65M22
- DOI: https://doi.org/10.1090/S0025-5718-2013-02678-6
- MathSciNet review: 3073187