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