Dissipativity of the linearly implicit Euler scheme for Navier‐Stokes equations with delay
Copyright policy )Dissipativity of the linearly implicit Euler scheme for Navier‐Stokes equations with delay
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. A by‐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.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2114–2140, 2017
- Changsha University of Science and Technology China (People's Republic of)
Method of lines for initial value and initial-boundary value problems involving PDEs, numerical attractors, Other numerical methods (fluid mechanics), Navier-Stokes equations with delay, Navier-Stokes equations for incompressible viscous fluids, Numerical solutions to abstract evolution equations, linearly implicit Euler scheme, dynamical systems, long-time stability, dissipativity
Method of lines for initial value and initial-boundary value problems involving PDEs, numerical attractors, Other numerical methods (fluid mechanics), Navier-Stokes equations with delay, Navier-Stokes equations for incompressible viscous fluids, Numerical solutions to abstract evolution equations, linearly implicit Euler scheme, dynamical systems, long-time stability, dissipativity
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!