In:
Numerical Methods for Partial Differential Equations, Wiley, Vol. 36, No. 6 ( 2020-11), p. 1389-1404
Abstract:
This paper utilizes the Picard method and Newton's method to linearize the stationary incompressible Navier–Stokes equations and then uses an LL* approach, which is a least‐squares finite element method applied to the dual problem of the corresponding linear system. The LL* approach provides an L 2 ‐approximation to a given problem, which is not typically available with conventional finite element methods for nonlinear second‐order partial differential equations. We first show that the proposed combination of linearization scheme and LL* approach provides an L 2 ‐approximation to the stationary incompressible Navier–Stokes equations. The validity of L 2 ‐approximation is proven through the analysis of the weak problem corresponding to the linearized Navier–Stokes equations. Then, the convergence is analyzed, and numerical results are presented.
Type of Medium:
Online Resource
ISSN:
0749-159X
,
1098-2426
Language:
English
Publisher:
Wiley
Publication Date:
2020
detail.hit.zdb_id:
2012605-0
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