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On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems
Author(s) -
Akbas M.,
Kaya S.,
Rebholz L. G.
Publication year - 2017
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.22061
Subject(s) - multiphysics , mathematics , stability (learning theory) , partial differential equation , compressibility , bounded function , crank–nicolson method , flow (mathematics) , mathematical analysis , finite element method , scheme (mathematics) , mechanics , geometry , physics , computer science , thermodynamics , machine learning
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. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 999–1017, 2017