Paper Info
Title
Convergence Analysis of a Finite Element Projection/Lagrange--Galerkin Method for the Incompressible Navier--Stokes Equations
Abstract
This paper provides a convergence analysis of a fractional-step method to compute incompressible viscous flows by means of finite element approximations. In the proposed algorithm, the convection, the diffusion, and the incompressibility are treated in three different substeps. The convection is treated first by means of a Lagrange--Galerkin technique, whereas the diffusion and the incompressibility are treated separately in two subsequent substeps by means of a projection method. It is shown that provided the time step, $\delta t,$ is of ${\cal O}(h^{d/4}),$ where $h$ is the meshsize and $d$ is the space dimension ($2\leq d \leq 3$), the proposed method yields for finite time T an error of ${\cal O}(h^{l+1}+\delta t)$ in the L2 norm for the velocity and an error of ${\cal O}(h^{l}+\delta t)$ in the H1 norm (or the L2 norm for the pressure), where l is the polynomial degree of the approximate velocity.
Year
DOI
Venue
2000
10.1137/S0036142996313580
SIAM J. Numerical Analysis
Keywords
Field
DocType
incompressible navier{stokes equations,proposed method yield,convergence analysis,stokes equations,finite element approximation,cal o,finite time,finite element projection,nite elements,galerkin method,l2 norm,lagrange{galerkin method,projection method,incompressible navier,h1 norm,fractional-step method,approximate velocity,different substeps,finite elements,finite element
Convergence (routing),Compressibility,Mathematical optimization,Mathematical analysis,Galerkin method,Degree of a polynomial,Finite element method,Projection method,Norm (mathematics),Mathematics,Navier–Stokes equations
Journal
Volume
Issue
ISSN
37
3
0036-1429
Citations 
PageRank 
References 
22
5.10
1
Authors
2
Name
Order
Citations
PageRank
Yves Achdou119732.74
J.-L. Guermond2507.96