CASCADIC MULTIGRID METHOD FOR THE MORTAR ELEMENT METHOD FOR P1 NONCONFORMING ELEMENT

In this paper,we consider the cascadic multigrid method for the mortar P_1 noncon-forming element which is used to solve the Poisson equation and prove that the cascadicconjugate gradient method is accurate with optimal complexity.     

旋转Q1非协调元的V循环多重网格法

1．引言近年来,多重网格法已成为行之有效的偏微分方程数值解法,而对非协调元的多重网格法也有众多的研究,例在[1,3］中,作者研究了非协P1元的w循环多重网格法,[10］中,作者研究了＊11s。n非协调元的V循环多重网格法．此外在K豆1,12］中,作者研究了板问题非协调有限元的多重网格法．最近,Rannacher和Turek同构造了所谓的QI非协调元,并用该元离散StokeS问题．而在问中,利用该元来计算晶体,数值效果非常好．同时在同中,作者给出了该元的误差估计和超收敛分析．最近,Chen和oswald同又讨论了该元的多重网格法,并证明了W循环…     

CONSTRAINED QUADRILATERAL NONCONFORMING ROTATED Q1 ELEMENT

In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated Q1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green＇s function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.     

NONCONFORMING QUADRILATERAL ROTATED ELEMENT FOR REISSNER-MINDLIN PLATE

In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.     

THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION

The mortar element method is a new domain decomposition method（DDM） with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H^1-norm estimates are obtained under a reasonable elliptic regularity assumption.     

A V-CYCLE MUTIGRID FOR QUADRILATERAL ROTATED Q1 ELEMENT WITH NUMERICAL INTEGRATION

In this paper, a V-cycle multigrid method is presented for quadrilateral rotated Q1 elements with numerical integration.     

MULTIGRID FOR THE MORTAR FINITE ELEMENT FOR PARABOLIC PROBLEM

In this paper, a mortar finite element method for parabolic problem is presented. Multi-grid method is used for solving the resulting discrete system. It is shown that the multigrid method is optimal, i.e, the convergence rate is independent of the mesh size L and the time step parameter τ.     

Reissner-Mindlin板问题带约束非协调旋转Q_1有限元方法

本文利用带约束非协调旋转Q_1元逼近Reissner-Mindlin板问题中旋度的两个分量.并分别选择Wilson元、双线性元和带约束非协调旋转Q_1元逼近挠度,相应地选取不连续的矢量值分片线性函数空间、最低阶旋转Raviart-Thomas元空间和矢量值分片常数函数空间为离散的剪应力空间,在矩形网格上构造了三个板元.通过证明一个离散的Korn不等式,并借助MITC4元的解构造了旋度、挠度和剪应力一个具有某种特殊且关键的可交换性的插值.再利用Helmholtz分解分析相容性误差.我们证明了这三个矩形元在能量范数意义下与板厚无关的一致最优收敛性.数值算例验证了我们的理论结果.     

MULTIGRID FOR THE MORTAR ELEMENT METHOD WITH LOCALLY P_1 NONCONFORMING ELEMENTS

In this paper we study the theoretical properties of multigrid algorithm for discretization of the Poisson equation in 2D using a mortar element method under the assumption that the triangulations on every subdomain are uniform. We prove the convergence of the W-cycle with a sufficiently large number of smoothing steps. The     

THE GENERALIZED MAXIMUM ANGLE CONDITION FOR THE Q1 ISOPARAMETRIC ELEMENT

We consider the quadrilateral Q1 isoparametric element and establish an optimal error estimate in H^1 norm for the interpolation operator under a weaker mesh condition which admits anisotropic quadrilaterals and allows the quadrilateral to become a regular triangle in the sense of maximum angle condition [5, 11].     

MORTAR型旋转Q_1元的多重网格方法

本文讨论了mortar型旋转Q_1元的多重网格方法.证明了W循环的多重网格法是最优的,即收敛率与网格尺寸及层数无关.同时给出了一种可变的V循环多重网格算法,得到了一个条件数一致有界的预条件子.最后,数值试验验证了我们的理论结果.     

MULTIGRID ALGORITHM FOR THE COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT METHOD AND FINITE ELEMENT METHOD FOR UNBOUNDED DOMAIN PROBLEMS

In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.     

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.     

Stokes问题的杂交-混合有限元分析

本文发展Stokes问题的一个四变量杂交-混合变分方程：应力-速度-压力-拉格朗日乘子．然后发展其有限元方法：对应四变量分别用间断型Raviart—Thomas最低阶元，分片常数元，连续线性元和连续线性元的迹空间．我们获得了稳定性和最优误差界．通过后处理办法，我们得到一个适合于计算的速度-压力格式，该格式可视为“Mini”元方法的一个变形(本文格式中引入了局部投影算子)．然而，本文格式关于压力具有“超收敛”结果：得到了压力关于H^1-范的误差界O(h)．     

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.     

A MPI PARALLEL PRECONDITIONED SPECTRAL ELEMENT METHOD FOR THE HELMHOLTZ EQUATION

Spectral element method is well known as high-order method, and has potential better parallel feature as compared with low order methods. In this paper, a parallel preconditioned conjugate gradient iterative method is proposed to solving the spectral element approximation of the Helmholtz equation. The parallel algorithm is shown to have good performance as compared to non parallel cases, especially when the stiffness matrix is not memorized. A series of numerical experiments in one dimensional case is carried out to demonstrate the efficiency of the proposed method.     

GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS

1. IntroductionIn the numerical simulation of the Navier-Stokes equations one encounters three seriousdifficulties in the case of large Reynolds numbers f the treatment of the incomPressibility con-dition divu = 0, the treatment of the noIilinear terms and the large time integration. For thetreatment of the incoInPressibility condition, one use the penalty method in the case of finiteelemellts [1--2l and for the treatmen of the noulinar terms and the large tfor integration, oneuse the nonlin…     

INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

1. IntroductionThe infinite element method has been successfully applied to some boundary valueproblems of partial differential equations, where the solutions possess corner singularpoints or the domains are exterior ones. If the equations are invariant under similaritytransformation the approaches have been given in [11] [131 for singular solutions, and in[12][15][181119] for the exterior problems. If the equations do not admit the above invariant property? one approach has been given in [14]…     

椭圆外区域上的自然边界元法

１．引言 二十年来,自然边界元法已在椭圆问题求解方面取得了许多研究成果。它可以直接用来解决圆内（外）区域、扇形区域、球内（外）区域及半平面区域等特殊区域上的椭圆边值问题［１,２,５］,也可以结合有限元法求解一般区域上的椭圆边值问题,例如基于自然边界归化的耦合算法及区域分解算法就是处理断裂区域问题及外问题的一种有效手段［２－４,６］。 人们在设计求解外问题的耦合算法或者区域分解算法时,通常选取圆周或球面作人工边界。但对具有长条型内边界的外问题,以圆周或球面作人工边界显然并非最佳选择,它将会导致大量的…     

非定常的热传导──对流问题的混合有限元法

1．引言设oCRZ是足够光滑的有界区域，考虑非定常的、无量纲化的，而且带有热传导的粘性不可压缩流体力学运动问题：问题（I）．求。＝（。1，。2），p，T满足；其中。是流体的速度向量，P为压力，T是温度，。＞0是运动粘性系数，入＞0是GroshoffM，j＝（0，1）是M维向量。x二hi，x。）·当温度T是常数时，问题（I）变为Navier－StokesIW题，而当！是常数时，问题（I）变为定常问题．到目前为止，对问题（I）的研究尚不多，只给出了一些计算方法（见11－4］等），对于有限元解的误差分析就更少．1994年，沈树民在问中首先对定常的问…