Stokes问题非协调混合有限元超收敛分析

本文通过引入全新的技巧,研究了Stokes问题的非协调混合有限元方法,得到了关于速度与压力的超逼近性质.进一步地通过构造一个恰当的插值后处理算子,还得到了关于速度的整体超收敛结果.     

Stokes流动的罚-杂交有限元分析*

本文建议了一种用于分析Stokes流动的罚-杂交变分原理,其中,偏应力张量和静水压力事先满足线动量平衡.建立了相应的有限元模型.由此,压力可在列式过程中消去,使得有限元矩阵方程仅以节点速度作为唯一的求解未知量.推导了几种4-节点和8-节点四边形单元.通过数值算例,显示了单元性能.     

Stokes问题的一种新的混合有限元逼近

为了求解Ｓｔｏｋｅｓ问题，本文构造出了一类新的满足ＢＢ－条件的有限元空间对，并给出了相应的超收敛分析．     

Stokes问题Q_2-P_1混合元外推方法

考虑Stokes问题的有限元解与精确解插值的Q2-P1混合元的渐近误差展开和分裂外推.首先利用积分恒等式技巧确定了微分方程精确解与有限元插值之间积分式的主项,其次再借助插值后处理和分裂外推技术,得到了比通常的误差估计提高两阶的收敛速度.     

求解Stokes问题的一类新混合元格式

利用Specht九参数元的分析技巧 ,通过对Adini元增加一个自由度 ,本文构造一类求解Stokes问题的新二阶混合有限元格式 .该格式简单实用且自由度较已有的许多二阶格式少 .     

Stokes问题各向异性网格Q2-P1混合元超收敛分析

讨论Stokes问题在各向异性冈格下的Q2-P1混合有限元方法，利用积分恒等式技巧得到了与传统方法相同的超逼近性质，同时基于插值后处理的技巧，构造了速度和压力的一对插值后处理算子，并且前者具有备向异性特征，从而导出了整体超收敛结果．     

无界区域上Stokes问题的自然边界元与有限元耦合法

§1.引言 对于用有限元方法求解平面有界区域上的Stokes问题,国内外已有大量工作,例如可见[2]、[9]及其所引文献.但对无界区域上的这一问题,由于区域的无界性给有限元方法带来了困难,边界元方法及边界元与有限元的耦合法便显示其优越性.本文提出用自然边界元与有限元的耦合法求解无界区域上的Stokes问题.这一耦合法早在作者以前的工作中被应用于求解调和问题、重调和问题和平面弹性问题,但将它用于求解     

Stokes问题的各向异性平行四边形有限元逼近

1 引言 Stokes问题是标准的混合问题,速度与压力同时计算,关于该问题有限元求解的文章很多(见文献[1-5])但大多都是基于对区域的正则剖分或拟一致剖分,即要求网格剖分满足hk/pK≤C,(A)K∈Jh,其中C>0为一常数,hk,pK分别为单元K的直径及内切园直径,在实际应用问题中,由于边界层或区域的拐角处需考虑物质的各向异性特征,此时对空间区域Q的剖分不再满足正则性或拟一致条件,而需要用各向异性网格剖分,才能更贴切地描述其真实情形.     

Stokes问题的一个非协调有限元

<正>1引言定常Stokes问题是流体力学中的一种重要问题,是标准的混合问题,速度与压力同时计算.关于该问题有限元求解的文章很多([1],[2],[4],[5],[6],[8],[9]),分析的难点在于单元必须满足离散的Babuska-Brezzi([2])条件.在([4])中提出了著名的非协调Crouzeix-Raviart     

ERROR ANALYSIS OF A STABILIZED FINITE ELEMENT METHOD FOR THE GENERALIZED STOKES PROBLEM

This paper is devoted to the establishment of sharper $a$ $priori$stability and error estimates of a stabilized finite element method proposed by Barrenechea and Valentin for solving the generalized Stokes problem, which involves a viscosity $\nu$ and a reaction constant $\sigma$. With the establishment of sharper stability estimates and the help of $ad$ $hoc$finite element projections, we can explicitly establish the dependence of error bounds of velocity and pressure on the viscosity $\nu$, the reaction constant $\sigma$, and the mesh size $h$. Our analysis reveals that the viscosity $\nu$ and the reaction constant $\sigma$ respectively act in the numerator position and the denominator position in the error estimates of velocity and pressure in standard norms without any weights. Consequently, the stabilization method is indeed suitable for the generalized Stokes problem with a small viscosity $\nu$ and a large reaction constant $\sigma$. The sharper error estimates agree very well with the numerical results.     

A MIXED FINITE ELEMENT METHOD FOR THE CONTACT PROBLEM IN ELASTICITY

Based on the analysis of [7] and [10], we present the mixed finite element approximation of the variational inequality resulting from the contact problem in elasticity. The convergence rate of the stress and displacement field are both improved from O（h3/4） to quasi-optimal O（h│logh│^1/4）. If stronger but reasonable regularity is available, the convergence rate can be optimal O（h）.     

THE NONCONFORMING FINITE ELEMENT METHOD FOR SIGNORINI PROBLEM

We present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. We show if the displacement field is of H2 regularity, then the convergence rate can be improved from O（h3/4） to quasi-optimal O（h｜log h｜1/4） with respect to the energy norm as that of the continuous linear finite element approximation. If stronger but reasonable regularity is available, the convergence rate can be improved to the optimal O（h） as expected by the linear approximation.     

解Stokes问题的P1非协调四边形元的稳定化方法

本文研究了用(~P)_1-Q_0元(其中(~P)_1表示P_1非协调四边形元)解Stokes问题的非协调混合有限元稳定化逼近方法.(~P)_1-Q_0元不满足LBB条件(见[7,14] ),因而其不能直接用来求解Stokes问题.受[3] 的启发,我们提出了一种用(~P)_1-Q_0元解Stokes问题的稳定化方法,证明了这种方法的稳定性和离散问题解的存在唯一性,得到了最优误差估计.文章最后给出的数值算例验证了我们的理论结果.     

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR SADDLE-POINT PROBLEM

1. IntroductionThere are many work to investigate the stability of the mired finite element methodfor the saddle-point problems, i.e., to construct the finite element spaces, such that theso-called discrete BB-codition is satisfied (c.f. [1],[21,[7],[81 and the references therein).To circumvent the discrete BB-conditon, recently there has been an increased interest inuse of least-squares approach for the solution of the mixed finite element approximationof the saddel-point problem (c.f.[3]--[…     

Stokes方程的稳定化间断有限元法

本文对定常的Stokes方程提出了一种新的间断有限元法,通过对通常的间断Galerkin有限元法应用稳定化思想,建立了一个相容的稳定间断有限元格式,对速度和压力的任意分片多项式空间Pl(K),Pm(K)的间断有限元逼近证明了解的存在唯一性,给出了关于速度和压力的L2 范数的最优误差估计．     

ACCURACY ENHANCEMENT FOR THE SIGNORINI PROBLEM WITH FINITE ELEMENT METHOD

In this paper,we study the accuracy enhancement for the frictionless Signorini problem on a polygonal domain with linear finite elements.Numerical test is given to verify our result.