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

Creative Commons License

AKBAŞ M., KAYA S., Rebholz L. G.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, vol.33, no.4, pp.999-1017, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1002/num.22061
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.999-1017
  • Keywords: Long time stability, Boussinesq, Magnetohydrodynamics, Navier-Stokes equations, finite element method, BDF2 timestepping, NAVIER-STOKES EQUATIONS, IMPLICIT EULER SCHEME, CRANK-NICOLSON, EFFICIENT, SYSTEM
  • Middle East Technical University Affiliated: Yes


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