Stokes问题非协调有限元逼近的最大模估计

本文考察了二维稳态和非稳态Stokes问题的基于速度—压力形式的非协调C-R逼近格式,利用Sobolev权模技巧和权模LBB条件,得到了稳态问题速度(包括它的梯度)和压力逼近解的拟最优的最大模估计,利用稳态问题结果和Stokes投影技巧,得到了非稳态问题速度(包括它的梯度)和压力的半离散逼近解的拟最优的最大模估计。     

ON THE ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT APPROXIMATION TO THE OBSTACLE PROBLEM

This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12].     

一类强非线性二阶椭圆问题混合元方法的最大模误差估计

本文利用正规格林函数及对偶论证技术证明了一类强非线性二阶椭圆问题混合方法对函数的Ｌ＾２投影具有几乎超收敛一阶的最大模误差估计,对伴随向量函数具有拟最优最大模误差估计。     

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     

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.     

INTERIOR ERROR ESTIMATES FOR NONCONFORMING FINITE ELEMENT METHODS OF THE STOKES EQUATIONS

1.IntroductionInteriorerrorestimatesforfiniteelementdiscretizations(conforming)werefirstintroducedbyNitscheandSchatz[14]forsecondorderscalarellipticequationsin1974.Theyprovedthatthelocalaccuracyofthefiniteelementapproximationisboundedintermsoftwofact...     

LOCAL AND PARALLEL FINITE ELEMENT ALGORITHMS FOR THE NAVIER-STOKES PROBLEM

Based on two-grid discretizations, in this paper, some new local and parallel finiteelement algorithms are proposed and analyzed for the stationary incompressible Navier-Stokes problem. These algorithms are motivated by the observation that for a solutionto the Navier-Stokes problem, low frequency components can be approximated well by arelatively coarse grid and high frequency components can be computed on a fine grid bysome local and parallel procedure. One major technical tool for the analysis is some locala priori error estimates that are also obtained in this paper for the finite element solutionson general shape-regular grids.     

不可压Navier-Stokes方程迎风格式及后验误差估计

1引言不可压Navier-Stokes方程作为流体力学的基本方程,其数值计算一直是科学与工程计算关心的问题．本文考虑定常问题: -ε△u (u·▽)u ▽p = f x∈Ω,▽·u=0 x∈Ω, (1) u =0 x∈(?)Ω．这里ε=1／Re是Reynolds数的倒数,u=(u1,u2,…,ud)为待求流速场,p是待求压力场,f=(f1,f2,…,fd)是给定的体力．Ωv(?) Rd(d=2,3)是有界区域,且具有分片Lipschitz连续边界(?)Ω．     

线性椭圆问题最低次混合有限元方法的最优最大模误差估计

本文对线性椭圆问题的最低次混合元方法提出了构造混合元空间的充分条件,并建立了新的插值算子.据此得到了混合元解,伴随向量函数及其散度的最优最大模误差估计.     

非协调板元的一般性误差估计式

１．引言 薄板弯曲问题对应于４阶椭圆边值问题,协调有限元求解此问题需要单元具有Ｃ~１连续性,这难于构造且应用不便,因此求解该问题主要应用非协调元．当非协调板元不具有 Ｃ０连续性时,标准能量模误差估计是 ,这一结果不理想,因为对一般的区域,甚至是凸多边形区域,真解只能属于 Ｈ３．近年来,企图将真解属于 Ｈ４的假定改为真解属于 Ｈ３的研究引起重视．针对最简单的三角形非协调板元－Ｍｏｒｌｅｙ元,石钟慈［２］在 Ｈ３假定下,直接利用非协调元分析技巧得到弯距和转角的误差估计式．本文将［２］的结果一般化,同时通过修…     

A NONCONFORMING ANISOTROPIC FINITE ELEMENT APPROXIMATION WITH MOVING GRIDS FOR STOKES PROBLEM

This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has anisotropic behavior and derive anisotropic error estimations in some certain norms of the velocity and the pressure based on some novel techniques. Especially through careful analysis we get an interesting result on consistency error estimation, which has never been seen for mixed finite element methods in the previously literatures.     

线性积分微分方程有限元逼近的最大模估计

1引言 考虑下述积分微分方程混合问题     

Navier－Stokes方程的变网格非协调有限元法

本文通过所谓的速度－压力型公式讨论了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的变网格非协调有限元逼近，得到了在确定模意义下的速度、压力误差估计，且在一定条件下，某些误差估计能达到最优。     

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.     

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.     

THE UPWIND FINITE ELEMENT SCHEME AND MAXIMUM PRINCIPLE FOR NONLINEAR CONVECTION-DIFFUSION PROBLEM

In this paper, a kind of partial upwind finite element scheme is studied for twodimensional nonlinear convection-diffusion problem. Nonlinear convection term approximated by partial upwind finite element method considered over a mesh dual to the triangular grid, whereas the nonlinear diffusion term approximated by Galerkin method. A linearized partial upwind finite element scheme and a higher order accuracy scheme are constructed respectively. It is shown that the numerical solutions of these schemes preserve discrete maximum principle. The convergence and error estimate are also given for both schemes under some assumptions. The numerical results show that these partial upwind finite element scheme are feasible and accurate.     

NONCONFORMING FINITE ELEMENT APPROXIMATIONS TOTHE UNILATERAL PROBLEM

1.IntroductionTherehavebeennumerousworkintheanalysisoffiniteelementmethodsfortheunilateralproblem(c.f.[4]andthereferencestherein).ItshouldbementionedthatinF.Scarpiniet.al.[6],I.Hlavaceket.al.[5]andF.Brezziet.al.[1],theconforminglinearelementapproximationtotheunilateralproblemhavebeenconsidered,andthevariouserrorboundshavebeenobtainedinthedifferentassumptionofregularityofsolutionoftheproblem.Inthispaper3weconsiderthreenonconformingfiniteelement(i.e.twoCrouzrixRaviartlinearelementsandWilsone…     

ON THE ERROR ESTIMATE OF LINEAR FINITE ELEMENT APPROXIMATION TO THE ELASTIC CONTACT PROBLEM WITH CURVED CONTACT BOUNDARY

1. PreliminaryThe error estimate of linear finite element approximation to the elastic contact problem with curved contact boundary was considered in [2], in which the authors obtainedthe error bound of O(hl) with a much complex proof, requirement of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2, Theorem 3.3, p.149]). In this paper, we obtained the error bound of O(hi) withonly requirement of two times continuously differentiable…