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

1.IntroductionThereismuchliteratureconcerningnumericalsolutionsofNavier-Stokesequations,e.g.,see[1--4].FOrsemi-periodicproblems,someauthorusedcombinedFOurierspectralfinitedifferenceandFOurierspectral--finiteelementapproximations(see[5--8]).Influiddyn...     

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.     

CHEBYSHEV PSEUDOSPECTRAL-HYBRID FINITE ELEMENT METHOD FOR THREE-DIMENSIONAL VORTICITY EQUATION

In this paper,Chebyshev pseudospectral-finite element schemes are proposed for solving three dimensional vorticity equation.Some approximation results in nonisotropic Sobolev spaces are given.The generalized stability and the convergence are proved strictly.The numerical results show the advantages of this method.The technique in this paper is also applicable to other three-dimensional nonlinear problems in fluid dynamics.     

THE CHEBYSHEV PSEUDOSPECTRAL DOMAIN DECOMPO SITION METHOD FOR SOLVING TWO-DIMENSIONAL ELLIPTIC EQUATION

This paper ix devoted to establishment of the Chebyshev pseudospectral domain de-composition scheme for solving two-dimensional elliptic equation. By the generalized equivalent variatiunal form, we can get the stability and convergence of this new scheme.     

THE ERRORS ESTIMATION OF THE CHEBYSHEV SPECTRAL－DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORTICITY EQUATION

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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…     

THE CHEBYSHEV SPECTRAL METHOD WITH A RESTRAINT OPERATOR FOR BURGERS EQUATION

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A C0-WEAK GALERKIN FINITE ELEMENT METHOD FOR THE TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS IN STREAM-FUNCTION FORMULATION

We propose and analyze a $C^0$-weak Galerkin (WG) finite element method for the numerical solution of the Navier-Stokes equations governing 2D stationary incompressible flows. Using a stream-function formulation, the system of Navier-Stokes equations is reduced to a single fourth-order nonlinear partial differential equation and the incompressibility constraint is automatically satisfied. The proposed method uses continuous piecewise-polynomial approximations of degree $k+2$ for the stream-function $\psi$ and discontinuous piecewise-polynomial approximations of degree $k+1$ for the trace of $\nabla\psi$ on the interelement boundaries. The existence of a discrete solution is proved by means of a topological degree argument, while the uniqueness is obtained under a data smallness condition. An optimal error estimate is obtained in $L^2$-norm, $H^1$-norm and broken $H^2$-norm. Numerical tests are presented to demonstrate the theoretical results.     

A MIXED FINITE ELEMENT METHOD ON A STAGGERED MESH FOR NAVIER-STOKES EQUATIONS

In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 - P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtained for both the velocity and the pressure. Numerical examples are presented to illustrate the effectiveness of the proposed method.     

非定常Navier-Stokes方程加罚形式的两重网格算法

A two-grid method (TGM) for the fully discrete unsteady NavierStokes (N-S) equations in a penalty form is discussed. An error estimate is given,and a numerical test is also given to verify the correctness of theoretical analysis.     

非稳态奇异系数微分方程的时间间断时空有限元方法

针对一类二维单轴奇异系数非稳态问题构造了一种时间间断时空有限元格式,利用以Radau点为节点的Lagrange插值多项式的特性,结合有限差分法和有限元法的技巧证明了格式的稳定性和有限元解的时间最大模、空间加权L²（?）-模误差估计.最后列举了一些数值试验结果,验证了理论结果和格式的可行性.     

非定常线性化Navier-Stokes方程的子格粘性非协调有限元方法

本文结合子格粘性法的思想,空间采用非协调Crouzeix-Raviart元逼近,时间采用Crank-Nicolson差分离散,对非定常线性化Navier-Stokes方程建立了全离散的子格粘性非协调有限元格式.对稳定性和误差估计作出了详细的分析, 得出了最优的误差估计.最后, 通过数值算例进一步验证了该方法的稳定性和收敛性.     

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.     

Webster方程有限元法的超收敛性

<正>1前言由语音生成过程建立的数学模型是一个无界区域上的声压波动方程,引入人工边界可将这个无界区域分成一个内部有界区域和另一个无界区域,再将时间和空间进行变量分离,就可以得到一个如下一维简单的基于内部有界区间的微分方程边值问题     

FOURIER PSEUDOSPECTRAL-FINITE DIFFERENCE METHOD FOR TWO-DIMENSIONAL VORTICITY EQUATION

A Fourier pseudospectral-finite difference sheme is proposed for solving two-dimensional vorticity equations.The generalized stability and the convergence are proved.The numerical results are given.     

FOURIER PSEUDOSPECTRAL－FINITE DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORICITY EQUATION

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FINITE ELEMENT NONLINEAR GALERKIN COUPLING METHOD FOR THE EXTERIOR STEADY NAVIER-STOKES PROBLEM

1.IntroductionNonlinearGalerkinmethodsaremultilevelschemesforthedissipativeevolutionpartialdifferentialequations.Theycorrespondtothesplittingsoftheunknownu:u=y z)wherethecomponentsareofdifferentorderofmagnitudewithrespecttoaparameterrelatedtothespati...     

MIXED FINITE ELEMENT METHODS FOR FRACTIONAL NAVIER-STOKES EQUATIONS

This paper gives the detailed numerical analysis of mixed finite element method for fractional Navier-Stokes equations.The proposed method is based on the mixed finite element method in space and a finite difference scheme in time.The stability analyses of semi-discretization scheme and fully discrete scheme are discussed in detail.Furthermore,We give the convergence analysis for both semidiscrete and flly discrete schemes and then prove that the numerical solution converges the exact one with order O(h2+k),where h and k:respectively denote the space step size and the time step size.Finally,numerical examples are presented to demonstrate the effectiveness of our numerical methods.     

REMARK ON GALERKIN METHOD FOR TWO-DIMENSIONAL STEADY STATE KURAMOTO-SIVASHINSKY EQUATION

1　IntroductionThe K-S equation represents a class of pattern formation equations.It has beenstudied extensively in recent years,both in the context of inertial manifolds and finite-di-mensional attractors as well as in numerical simulations of system dynamical behaviour( see[2 ,4 ,7-1 0 ] ) .Despite many studies of dynamical behaviour of the K_ Sequation,the steady-state analysis of the equation has not been thoroughly carried out,which ispractically important and theoretically interesting.…