TY - JOUR
T1 - Taylor Expansion Algorithm for the Branching Solution of the Navier-Stokes Equations
AU - K. Li & Y. He
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 459
EP - 478
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/941.html
KW - nonlinear operator equation, the Navier-Stokes equations, Taylor expansion algorithm, optimum nonlinear Galerkin method.
AB - <p style="text-align: justify;">The aim of this paper is to present a general algorithm for
the branching solution of nonlinear operator equations in a Hilbert
space, namely the $k$-order Taylor expansion algorithm, $k \geq 1$. The
standard Galerkin method can be viewed as the 1-order Taylor expansion
algorithm; while the optimum nonlinear Galerkin method can be viewed as
the 2-order Taylor expansion algorithm. The general algorithm is then
applied to the study of the numerical approximations for the steady
Navier-Stokes equations. Finally, the theoretical analysis and numerical
experiments show that, in some situations, the optimum nonlinear
Galerkin method provides higher convergence rate than the standard
Galerkin method and the nonlinear Galerkin method.</p>