Second-Order Convergence of the Linearly Extrapolated Crank–Nicolson Method for the Navier–Stokes Equations with H1 Initial Data

Buyang Li, Shu Ma, Na Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with H1 initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank–Nicolson scheme, with the usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.

Original languageEnglish
Article number70
Pages (from-to)1-20
Number of pages20
JournalJournal of Scientific Computing
Volume88
Issue number3
DOIs
Publication statusPublished - Sep 2021

Keywords

  • Error estimate
  • Linearly extrapolated Crank–Nicolson method
  • Locally refined stepsizes
  • Navier–Stokes equations
  • Nonsmooth initial data

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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