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Adaptive Wavelet Solution to the stokes problem

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 613-626页

作者： Ying-chun Jiang Youming Liu College of Mathematics and Computer Sciences Guilin University of Electronic Technology Cuilin 541004 China Department of Applied Mathematics Beijing University of Technology Beijing 100022 China

This paper deals with the design and analysis of adaptive wavelet method for the stokes problem. First, the limitation of Richardson iteration is explained and the multiplied matrix M0 in the paper of Bramble and Pasciak is proved to be the simplest possible in an appropiate sense. Similar to the divergence operator, an exact application of its dual is shown; Second, based on these above observations, an adaptive wavelet algorithm for the stokes problem is designed. Error analysis and computational complexity are given; Finally, since our algorithm is mainly to deal with an elliptic and positive definite operator equation, the last section is devoted to the Galerkin solution of an elliptic and positive definite equation. It turns out that the upper bound for error estimation may be improved.

关键词： Richardson iteration adaptive algorithm wavelets stokes problem Galerkin solution

LOCALLY STABILIZED FINITE ELEMENT METHOD FOR stokes problem WITH NONLINEAR SLIP BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2010年第6期28卷 826-836页

作者： Yuan Li Kai-tai Li College of Mathematics and Information Science Wenzhou University Wenzhou 325035 China School of Science Xi'an Jiaotong University Xi'an 710049 China School of Science Xi'an Jiaotong University Xi'an 710049 China

Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.

关键词： stokes problem Nonlinear Slip Boundary Variational Inequality Local Stabilized Finite Element Method Error Estimate.

Composite penalty method of a low order anisotropic nonconforming finite element for the stokes problem

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Applied Mathematics(A Journal of Chinese Universities) 2013年第1期28卷 49-56页

作者： WU Jing-zhu XING Xiu-zhi SHI Dong-yang Department of Mathematics Zhoukou Normal University Department of Mathematics Zhengzhou University

Composite penalty method of a low order anisotropic nonconforming quadrilateral finite element for the stokes problem is presented. This method with a large penalty parameter can achieve the same accuracy as the stand method with a small penalty parameter and the convergence rate of this method is two times as that of the standard method under the condition of the same order penalty parameter. The superconvergence for velocity is established as well. The results of this paper are also valid to the most of the known nonconforming finite element methods.

关键词： stokes problem composite penalty method anisotropic mesh.

CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE stokes problem

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Applied Mathematics and Mechanics(English Edition) 2002年第10期23卷 1207-1214页

作者：罗振东朱江 Department of Mathematics Capital Normal University Beijing P R China ICCES Institute of Atmospheric Physics Chinese Academy of Sciences Beijing P R China

Two simplified and stabilized mixed element formats for the stokes problem are derived by bubble function, and their convergence, i.e., error analysis, are proved. These formats can save more freedom degrees than othe... 详细信息

关键词： stokes problem stabilized format mixed element format error analysis

A Finite Volume Method Based on the Constrained Nonconforming Rotated Q_(1)-Constant Element for the stokes problem

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Advances in Applied Mathematics and Mechanics 2012年第1期4卷 46-71页

作者： Jing Qi Wanfu Tian Yonghai Li Jilin University Changchun 130012China School of Mathematics Jilin UniversityChangchun 130012China School of Science Shenyang Aerospace UniversityShenyang 110136China

We construct a finite volume element method based on the constrained nonconforming rotated Q_(1)-constant element(CNRQ_(1)-P_(0))for the stokes *** meshes are needed,which are the primal mesh and the dual *** approximate the velocity by CNRQ_(1)elements and the pressure by piecewise *** errors for the velocity in the H^(1)norm and for the pressure in the L^(2)norm are O(h)and the error for the velocity in the L^(2)norm is O(h^(2)).Numerical experiments are presented to support our theoretical results.

关键词： stokes problem finite volume method constrained nonconforming rotated Q_(1)element

DIVERGENCE - FREE WAVELET SOLUTION TO THE stokes problem

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Analysis in Theory and Applications 2007年第1期23卷 83-91页

作者： Yingchun Jiang Department of Applied Mathematics Beijing University of Technology Pingle Yuan 100 Beijing 100022 P. R. China

In this paper, we use divergence-free wavelets to give an adaptive solution to the velocity field of the stokes problem. We first use divergence-free wavelets to discretize the divergence-free weak formulation of the stokes problem and obtain a discrete positive definite linear system of equations whose coefficient matrix is quasi-sparse; Secondly, an adaptive scheme is used to solve the discrete linear system of equations and the error estimation and complexity analysis are given.

关键词： divergence-free wavelet stokes problem adaptive solution

A Nonconforming Rectangular Finite Element Analysis for the stokes problem

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Chinese Quarterly Journal of Mathematics 2009年第4期24卷 621-627页

作者： XIAO Liu-chao CHEN Shao-chun College of Science Henan University of Technology Zhengzhou 450001 China Department of Mathematics Zhengzhou University Zhengzhou 450001 China

A nonconforming rectangular finite element is presented, which satisfies the discrete B-B condition for the stokes problem. And the element has two order convergence rate for the velocity and pressure.

关键词： stokes problem nonconforming finite element B-B condition

Analysis on a Finite Volume Element Method for stokes problems

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Acta Mathematicae Applicatae Sinica 2005年第3期21卷 359-372页

作者： Hong-xing Rui School of Mathematics and Systems Science Shandong University Jinan 250100 China

Finite volume element method for the stokes problem is considered. We use a conforming piecewise linear function on a fine grid for velocity and piecewise constant element on a coarse grid for pressure. For general triangulation we prove the equivalence of the finite volume element method and a saddle-point problem, the inf-sup condition and the uniqueness of the approximation solution. We also give the optimal order H^1 norm error estimate. For two widely used dual meshes we give the L^2 norm error estimates, which is optimal in one case and quasi-optimal in another ease. Finally we give a numerical example.

关键词： Finite volume element stokes problem numerical analysis

stokes问题混合元方法中数值积分的影响

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高等学校计算数学学报 1999年第2期21卷 150-154页

作者：王烈衡罗振东李雅如中国科学院计算数学与科学工程计算研究所科学工程计算国家重点实验室!北京100080

in this paper, for the mixed finite element methods of stokes problem, such as the mini element and the scecon cider scheme, we present the numerical quadratures, which are independent of the bubble term. The effect a... 详细信息

关键词： stokes problem bubble function numerical quadrature