Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Detail(s)

Original languageEnglish
Pages (from-to)139-161
Journal / PublicationNumerische Mathematik
Volume134
Issue number1
Online published26 Oct 2015
Publication statusPublished - Sep 2016

Abstract

The paper is concerned with the unconditional stability and convergence of characteristics type methods for the time-dependent Navier–Stokes equations. We present optimal error estimates in L2 and H1 norms for a typical modified characteristics finite element method unconditionally, while all previous works require certain time-step restrictions. The analysis is based on an iterated characteristic time-discrete system, with which the error function is split into a temporal error and a spatial error. With a rigorous analysis to the characteristic time-discrete system, we prove that the difference between the numerical solution and the solution of the time-discrete system is τ-independent, where τ denotes the time stepsize. Thus numerical solution in W1 , is bounded and optimal error estimates can be obtained in a traditional way. Numerical results confirm our analysis and show clearly the unconditional stability and convergence of the modified characteristics finite element method for the time-dependent Navier–Stokes equations. The approach used in this paper can be easily extended to many other characteristics-based methods.

Research Area(s)

  • 35K61, 65N12, 65N30, 76M10