A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier–Stokes equations

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Abstract

We prove that for a given smooth initial value, if a finite element solution of the three-dimensional Navier–Stokes equations is bounded in a certain norm with a relatively small mesh size, then the solution of the Navier–Stokes equations with this given initial value must be smooth and unique, and is successfully approximated by the numerical solution.

Original languageEnglish
Pages (from-to)283-304
Number of pages22
JournalNumerische Mathematik
Volume147
Issue number2
DOIs
Publication statusPublished - Feb 2021

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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