On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems

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2017-07-01
We prove long-time stability of linearly extrapolated BDF2 (BDF2LE) timestepping methods, together with finite element spatial discretizations, for incompressible Navier-Stokes equations (NSE) and related multiphysics problems. For the NSE, Boussinesq, and magnetohydrodynamics schemes, we prove unconditional long time L-2 stability, provided external forces (and sources) are uniformly bounded in time. We also provide numerical experiments to compare stability of BDF2LE to linearly extrapolated Crank-Nicolson scheme for NSE, and find that BDF2LE has better stability properties, particularly for smaller viscosity values. (c) 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 999-1017, 2017
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

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Citation Formats
M. AKBAŞ, S. Kaya, and S. Kaya Merdan, “On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems,” NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, pp. 999–1017, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39892.