一类非线性椭圆问题的瀑布型多重网格法

本对二阶非线性椭圆问题提出一种瀑布型多重网格法，数值实验表明该算法非常有效，当d＝1时，给出了理论结果。     

CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS

1. IntroductionBornemann and Deuflhaxd [2][3] have Presented a new take of multgiid methods,the sthcalled cascadic multigrid. Compared with usual multigrid ndhods, it reqno coarse grid correCtions at all that may be viewed as a "one way" multis. AnotherdiStinctive feature is performing more iterations on coarser levels so as to obtain leSSiterations on finer levels. Numerical openments show that this ndhod is yak effectivefor second order elliptic problems.In the paper3 we will consider the…     

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.     

REVIEW ARTICLE MULTIGRID METHODS FOR OBSTACLE PROBLEMS

In this review, we intend to clarify the underlying ideas and the relations between various multigrid methods ranging from subset decomposition, to projected subspace decomposition and truncated multigrid. In addition, we present a novel globally convergent inexact active set method which is closely related to truncated multigrid. The numerical properties of algorithms are carefully assessed by means of a degenerate problem and a problem with a complicated coincidence set.     

MULTIGRID METHODS FOR OBSTACLE PROBLEMS

In this review,we intend to clarify the underlying ideas and the relations between various multigrid methods ranging from subset decomposition,to projected subspace decomposition and truncated multigrid.In addition,we present a novel globally convergent inexact active set method which is closely related to truncated multigrid.The numerical properties of algorithms are carefully assessed by means of a degenerate problem and a problem with a complicated coincidence set.     

ON CONVERGENCE OF MULTIGRID METHOD FOR NONNEGATIVE DEFINITE SYSTEMS

In this paper, we consider multigrid methods for solving symmetric nonnegative definite matrix equations. We present some interesting features of the multigrid method and prove that the method is convergent in L2 space and the convergent solution is unique for such nonnegative definite system and given initial guess.     

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.     

MULTIGRID METHODS FOR MORLEY ELEMENT ON NONNESTED MESHES

1.IntroductionWeconsidersomemultigridalgorithmsforthebiharmonicequationdiscretizedbyMoneyelementonnonnestedmeshes.TOdefineamultigridalgorithm,certainintergridtransferoperatorhastobeconstructed.Throughtakingtheaveragesofthenodalvariables,weconstructanintergridtransferoperatorforMoneyelementonnonnestedmeshesthatsatisfiesacertainstableapproximationpropertywhichplaysakeyroleinmultigridmethodsfornonconformingplateelementsonnonnestedmeshes.Theso--calledregularity-approximaticnassurnptionisestablis…     

CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

1. IntroductionSpectral method has been used successfu11y in computational fluid dynamics. FOr semi-periodic problems, we can use mixed FOurier-Chebyshev spectral method, FOurier spectral-finitedifference method and FOurier spectral-finite element method …     

对流扩散方程一类改进的特征线修正有限元方法

１引言在地下水污染,地下渗流驱动,核污染,半导体等问题的数值模拟中,均涉及抛物型对流扩散方程（或方程组）的数值求解问题．这些对流扩散型偏微分方程（或方程组）具有共同的特点：对流的影响远大于扩散的影响,即对流占优性,对流占优性给问题的数值求解带来许多困难,因此对流占优问题的有效数值解法一直是计算数学中重要的研究内容．用通常的差分法或有限元法进行数值求解将出现数值振荡．为了克服数值振荡,提出各种迎风方法和修正的特征方法并在这些问题上得到成功的实际应用、８０年代,Ｄｏｕｇｌａｓ和Ｒｕｓｓｅｌｌ［２］等…     

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…     

DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EQUATIONS

1. IlltroductionThe finite element approximation of the convection--diffusin equations has been investigated using several different approaches (see e.g. [3] [4] and the references therein).Previous analysis in primal formulation of these problems was done for two types ofapproximation schemes: one which produces a continuous piecewise polynomial approximation and one which produces a piecewise polynomial approximation which arecontinuous for certain number of moments accross interelement edge…     

一类非对称椭圆问题瀑布型多重网格法

本将瀑布型多重网格法用于求解非对称椭圆边值问题，数值结果表明算法是有效的。     

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]…     

STABILIZED FEM FOR CONVECTION-DIFFUSION PROBLEMS ON LAYER-ADAPTED MESHES

The application of a standard Galerkin finite element method for convection-diffusion problems leads to oscillations in the discrete solution, therefore stabilization seems to be necessary. We discuss several recent stabilization methods, especially its combination with a Galerkin method on layer-adapted meshes. Supercloseness results obtained allow an improvement of the discrete solution using recovery techniques.     

LEGENDRE SPECTRAL-FINITE ELEMENT METHOD FOR THE THREE-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

This paper is devoted to the mixed Legendre spectral-finite element approximation of the three-dimensional, non-periodic, unsteady Navier-Stokes equations. A class of fully discrete schemes are constructed with artificial compression. The generalized stability and convergence are proved strictly on the assumption that the two-dimensional inf-sup condition of the finite element approximation is satisfied.     

抛物方程时间周期问题的有限元多格子动力学迭代

本文我们研究线性周期抛物方程的有限元多格子动力学迭代.多格子动力学迭代又称多重网格波形松弛,它是在函数空间中的一种迭代过程.对于由加速技术得到的多格子动力学迭代算子,我们通过计算周期函数的Fourier系数给出了新的谱表达式.从这些有用的表达式出发,我们推导了时间连续和离散格式的迭代收敛条件.数值实验进一步验证了本文的理论结果.     

非对称椭圆型变分问题的多重网格法

1.引言 多重网格法是求解椭圆型方程边值问题的一种有效的迭代解法,其特点是方法收敛速度与网格长度h无关,因此为达到具有相同精度的解只需O(N)次的运算量(N为离散后的线性方程组未知数个数).从而比一般的迭代法有效得多.现在这个方法已被广泛