摘要
本文的目的是给出一种解Hilbert空间中非线性方程的k阶泰勒展式算法(k1).标准Galerkin方法可以看作1阶泰勒展式算法,而最优非线性Galerkin方法可视为2阶泰勒展式算法.我们应用这种算法于定常的Navier-Stokes方程的数值逼近.在一定情景下,最优非线性Galerkin方法提供比标准Galerkin方法和非线性Galerkin方法更高阶的收敛速度.
The aim of this paper is to present a general algorithm for solving the nonlinear operator equations in a Hilbert space, namely the k -order Taylor expansion algorithm, k1 . 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 convergencerate than the standard Galerkin method and nonlinear Galerkin method.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
1998年第2期317-326,共10页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金
基础研究攀登计划
关键词
非线性
算子方程
泰勒展式算法
N-S方程
Nonlinear operator equation, Navier-Stokes equations, Taylor expansion algorithm, Optimum nonlinear Galerkin method