Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in R2 with L2 Initial Data
In this paper, we study the finite element method of the Navier–Stokes equations with the initial data belonging to the L2 space for all time t>0. Due to the poor smoothness of the initial data, the solution of the problem is singular, although in the H1-norm, when t∈[0,1). Under the uniqueness c...
Gespeichert in:
Veröffentlicht in: | Entropy (Basel, Switzerland) Switzerland), 2023-04, Vol.25 (5), p.726 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | In this paper, we study the finite element method of the Navier–Stokes equations with the initial data belonging to the L2 space for all time t>0. Due to the poor smoothness of the initial data, the solution of the problem is singular, although in the H1-norm, when t∈[0,1). Under the uniqueness condition, by applying the integral technique and the estimates in the negative norm, we deduce the uniform-in-time optimal error bounds for the velocity in H1-norm and the pressure in L2-norm. |
---|---|
ISSN: | 1099-4300 1099-4300 |
DOI: | 10.3390/e25050726 |