TAYLOR EXPANSION ALGORITHM FOR THE BRANCHING SOLUTION OF THE NAVIER-STOKES EQUATIONS
TAYLOR EXPANSION ALGORITHM FOR THE BRANCHING SOLUTION OF THE NAVIER-STOKES EQUATIONS
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发表时间：
2005
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通讯作者：
Kaitai Li;Yinnian He
中科院分区：
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作者：
Kaitai Li;Yinnian He
本文的目的是提出一种希尔伯特空间中非线性算子方程分支解的通用算法，即k阶泰勒展开算法，k� 1。标准伽辽金方法可以看作是一阶泰勒展开算法；而最优的非线性Galerkin方法可以看作是2阶泰勒展开算法。然后将通用算法应用于稳态纳维-斯托克斯方程的数值近似研究。最后，理论分析和数值实验表明，在某些情况下，最优非线性伽辽金方法比标准伽辽金方法和非线性伽辽金方法具有更高的收敛速度。
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� 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 al- gorithm. 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.