Global finite element nonlinear galerkin method for the penalized navier-stokes equations

Yin-nian He; Yan-ren Hou; Li-quan Mei

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Global finite element nonlinear galerkin method for the penalized navier-stokes equations

机译：惩罚Navier-stokes方程的全局有限元非线性Galerkin方法

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A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces X_H and X_h, defined respectively on one coarse grid with grid size H and one fine grid with grid size h ＜＜H. Comparison is also made with the finite element Galerkin method. If we choose H=O (ε~-1/4h~1/2), ε＞0 being the penalty parameter, then two methods are of the same Order of approximation. However, the global finite element nonlinear Galerkin method Is much cheaper than the standard finite element Galerkin method.

机译：提出了惩罚Navier-Stokes方程的全局有限元非线性Galerkin方法。该方法基于两个有限元空间X_H和X_h，分别在一个网格尺寸为H的粗网格和一个网格尺寸h ＜＜ H的精细网格上定义。还与有限元Galerkin方法进行了比较。如果我们选择H = O（ε〜-1 / 4h〜1/2），ε＞ 0作为惩罚参数，那么两种方法的近似阶数相同。但是，全局有限元非线性Galerkin方法比标准有限元Galerkin方法便宜得多。

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来源
《Journal of Computational Mathematics》 |2001年第6期|p.607-616|共10页
作者
Yin-nian He; Yan-ren Hou; Li-quan Mei;
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原文格式 PDF
正文语种 eng
中图分类计算数学;
关键词
Nonlinear Galerkin method; Finite element; Penalized Navier-Stokes equations;

机译：非线性Galerkin方法;有限元;罚纳维-斯托克斯方程;

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专利

1. An Optimal Nonlinear Galerkin Method with Mixed Finite Elements for the Steady Navier-Stokes Equations [J] . Yinnian He, Aiwen Wang, Zhangxin Chen, Numerical Methods for Partial Differential Equations: An International Journal . 2003,第6期

机译：稳态Navier-Stokes方程的混合有限元最优非线性Galerkin方法
2. Convergence and stability of finite element nonlinear Galerkin method for the Navier-Stokes equations [J] . He YN., Li KT. Numerische Mathematik . 1998,第1期

机译：Navier-Stokes方程的有限元非线性Galerkin方法的收敛性和稳定性
3. Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair [J] . D. Xiao, F. Fang, J. Du, Computer Methods in Applied Mechanics and Engineering . 2013,第MARa1期

机译：使用混合有限元对的Navier-Stokes方程降阶建模的非线性Petrov-Galerkin方法
4. Lagrange-Galerkin Discontinuous Finite Element Methods for the Navier-Stokes Equations [C] . Yan Luo, You-cai Xu 2010 International Conference on Computational and Information Sciences . 2010

机译：Navier-Stokes方程的Lagrange-Galerkin间断有限元方法
5. Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations. [D] . Arteaga, Santiago Egido. 1998

机译：不可压缩Navier-Stokes方程的有限元离散化的非线性和并行算法。
6. Numerical Analysis of an H1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation [O] . Jinfeng Wang, Meng Zhao, Min Zhang, -1

机译：H的数值分析时间分数电报方程的1-Galerkin混合有限元方法
7. Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations [O] . Ali Ait Ou Ammi, Ali Ait, Ou Ammi, 1994

机译：非线性Galerkin方法和混合有限元：Navier-stokes方程的双网格算法

Global finite element nonlinear galerkin method for the penalized navier-stokes equations

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