On the unconditional long-time L2-stability of the BDF2 time stepping scheme for the two-dimensional Navier-Stokes equations

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-04-01 DOI:10.1016/j.apnum.2025.03.008

Ming-Cheng Shiue

引用次数: 0

Abstract

In this note, we study the long-time

L^{2}

stability of the BDF2 time stepping scheme for the two-dimensional Navier-Stokes equations with homogenous Dirichlet boundary condition. More precisely, the numerical scheme obtained from using the backward differentiation formula (BDF2) in time is proven to be long time stable in

L^{2}

for any size of the time step

Δ t > 0

. In addition, less regularity of the solution is required to derive the unconditional long-time

L^{2}

stability of the BDF2 time stepping scheme. This improves the results in [1] and [9].

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.