加罚Navier-Stokes方程的最佳非线性Galerkin算法

数学物理学报 ›› 1998, Vol. 18 ›› Issue (3): 251-256.

加罚Navier-Stokes方程的最佳非线性Galerkin算法

何银年

西安交通大学应用数学研究中心西安 710049

收稿日期:1996-08-19 修回日期:1997-01-03 出版日期:1998-09-26 发布日期:1998-09-26
基金资助:
国家自然科学基金和西安交通大学科研基金资助

Optimum Nonlinear Galerkin Algorithm for the Penalized Navier-Stokes Equations

He Yinnian

Research Center for Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049

Received:1996-08-19 Revised:1997-01-03 Online:1998-09-26 Published:1998-09-26

摘要/Abstract

摘要： 该文提出了求解二维加罚Navier-Stokes方程的最佳非线性Galerkin算法.这个算法在于在粗网格有限元空间X_H⊂X_h(h<H)上求解一非线性子问题,在细网格增量有限元空间W_h上求解一线性子问题.如果线性有限元被使用及H=o(ε^(-1/4)h^1/2),则该算法具有和有限元Galerkin算法同阶的收敛速度.然而该文提出的算法可以节省可观的计算时间.

关键词: 加罚Navier-Stokes方程, 非线性Galerkin算法有限元

Abstract: This paper presents a optimum nonlinear Galerkin algorithm for solving the two-dimensional penalized Navier-Stokes equations. The algorithm consists in solving a nonlinear subproblem on a coarse grid finite element space X_H⊂X_h(h<H) and solving a linear subproblem on a fine grid incremental finite element space W_h. If the linear finite elements are used and H=o(ε^(-1/4)h^1/2), then the algorithm is of the convergence rate of same order as the finite element Galerkin algorithm. However, this algorithm can save a large amount of computing time.

Key words: Penalized Navier-Stokes equations, Finite element, Nonlinear Galerkin algorithm

何银年. 加罚Navier-Stokes方程的最佳非线性Galerkin算法[J]. 数学物理学报, 1998, 18(3): 251-256.

He Yinnian. Optimum Nonlinear Galerkin Algorithm for the Penalized Navier-Stokes Equations[J]. Acta mathematica scientia,Series A, 1998, 18(3): 251-256.