Stability of the Crank–Nicolson–Adams–Bashforth scheme for the 2D Leray‐alpha model |
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| Authors: | Monica Morales Hernandez Leo G Rebholz Cristina Tone Florentina Tone |
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| Affiliation: | 1. Department of Mathematical Sciences, Clemson University, Clemson, South Carolina;2. Department of Mathematics, University of Louisville, Louisville, Kentucky;3. Department Mathematics and Statistics, University of West Florida, Pensacola, Florida |
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| Abstract: | We consider the stability of an efficient Crank–Nicolson–Adams–Bashforth method in time, finite element in space, discretization of the Leray‐α model. We prove finite‐time stability of the scheme in L2, H1, and H2, as well as the long‐time L‐stability of the scheme under a Courant‐Freidrichs‐Lewy (CFL)‐type condition. Numerical experiments are given that are in agreement with the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1155–1183, 2016 |
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| Keywords: | Crank– Nicolson– Adams– Bashforth scheme discrete Gronwall lemmas Leray‐alpha model |
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