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

Buyang Li

doi:10.1007/s00211-021-01172-0

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

Buyang Li

Research output: Journal article publication › Journal article › Academic research › peer-review

6 Citations (Scopus)

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 language	English
Pages (from-to)	283-304
Number of pages	22
Journal	Numerische Mathematik
Volume	147
Issue number	2
DOIs	https://doi.org/10.1007/s00211-021-01172-0
Publication status	Published - Feb 2021

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1007/s00211-021-01172-0

http://hdl.handle.net/10397/93876

Cite this

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AB - 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.

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

Abstract

ASJC Scopus subject areas

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