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.
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