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- Title
Dissipativity of the Linearly Implicit Euler Scheme for Navier-Stokes Equations with Delay.
- Authors
Wang, Wansheng
- Abstract
In this article, we study the dissipativity of the linearly implicit Euler scheme for the 2D Navier-Stokes equations with time delay volume forces (NSD). This scheme can be viewed as an application of the implicit Euler scheme to linearized NSD. Therefore, only a linear system is needed to solve at each time step. The main results we obtain are that this scheme is L² dissipative for any time step size and H¹ dissipative under a time-step constraint. As a consequence, the existence of a numerical attractor of the discrete dynamical system is established. Aby-product of the dissipativity analysis of the linearly implicit Euler scheme for NSD is that the dissipativity of an implicit-explicit scheme for the celebrated Navier-Stokes equations that treats the volume forces term explicitly is obtained.
- Subjects
EULER equations; NAVIER-Stokes equations; TIME delay systems; DYNAMICAL systems; DISCRETE systems; LINEAR systems
- Publication
Numerical Methods for Partial Differential Equations, 2017, Vol 33, Issue 6, p2114
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22182