Stability of the Crank–Nicolson–Adams–Bashforth scheme for the 2D Leray‐alpha model | Zendy

Morales Hernandez Monica | Zendy; Rebholz Leo G. | Zendy; Tone Cristina | Zendy; Tone Florentina | Zendy

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Stability of the Crank–Nicolson–Adams–Bashforth scheme for the 2D Leray‐alpha model

Author(s) -

Morales Hernandez Monica,

Rebholz Leo G.,

Tone Cristina,

Tone Florentina

Publication year - 2016

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.22045

Subject(s) - crank–nicolson method , linear multistep method , mathematics , discretization , stability (learning theory) , scheme (mathematics) , partial differential equation , finite element method , stability conditions , mathematical analysis , ordinary differential equation , differential equation , thermodynamics , computer science , discrete time and continuous time , physics , differential algebraic equation , machine learning , statistics

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 L 2 , H 1 , and H 2 , 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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