A HIGH ACCURACY ANALYSIS OF THE MIXED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATIONS

In this paper,the linear mixed finite element method is considered forthe biharmonic Dirichlet boundary value problem.Almost optimal error estimates,superconvergence estimates and the derivative error expansion are obtained.     

HIGHLY NONCONFORMING FINITE ELEMENT APPROXIMATIONS FOR A FOURTH ORDERVARIATIONAL INEQUALITY WITH CURVATURE OBSTACLE

The purpose of this paper is to obtain the optimal error estimates of O(h) for the highly nonconforming elements to a fourth order variational inequality with curvature obstacle in a convex domain with simply supported boundary by using the novel function splitting method and the orthogonal properties of the nonconforming finite element spaces.Morley‘s element approximation is our special case.     

FINITE ELEMENT METHOD AND ANALYSIS FOR CHEMICAL-FLOODING SIMULATION

1.IntroductionThisarticlediscussestheenhanced0ilrecoverynumericalsimulationofthechemicalflood-ing(suchassurfactats,alcohol,polymers)c0mposed0f3-dimensional,multicomponent,muLtiphaseandincompressiblemixedfluids.Aftertheoilfieldiswaterfi0oded,thereisstillalargeamountofcrudeoilleftintheoildeposit.Thisamountofoil,boundedbycapillarypressure,cannotflow;or)asaresultofthedisadvantageousrateofflowbetweenthedisplacinganddisplacedphases,thevolumethattheinjectionfiowaffectsistoosmalltodrivethecrudeoil.By…     

GLOBAL SUPERCONVERGENCE ANALYSIS OF WILSON ELEMENT FOR SOBOLEV AND VISCOELASTICITY TYPE EQUATIONS

In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-uniform rectangular meshes. Finally, an error correction scheme is presented.     

系统分析中结构建模的核心变换法

核心变换法是作者提出的“核心要素法”体系中的基本方法之一，是结构建模中消除未知元素的一种非常有效的新方法，这种方法从初始矩阵开始，利用传递性经过一系列的“核心变换”，消除未知关系从而得到可达矩阵表示的结构模型。     

THE SUPERCONVERGENCE ANALYSIS OF AN ANISOTROPIC FINITE ELEMENT

This paper deals with the high accuracy analysis of bilinear finite element on the class of anisotropic rectangular meshes. The inverse inequalities on anisotropic meshes are established. The superclose and the superconvergence are obtained for the second order elliptic problem. A numerical test is given, which coincides with our theoretical analysis.     

GLOBAL SUPERCONVERGENCE FOR A MIXED FINITE ELEMENT METHOD FOR THE WAVE EQUATION

1.IntroductionWeconsiderthesecondorderhyperbolicequationwithinitialconditionswhereaCRZisaboundeddomainwithboundariesparalleltotheaxes.Forconvenience,weassumehomogeneousDirichletboundaryconditions'Weassumethatthefunctionsailandfareuniformlyboundedandmeasurable,andthespatialoperatorisuniformlyellipticinthesensethatthereexistpositiveconstantsorandPsuchthatInamixedfiniteelementformulationbothdisplacementsandstressesareapproximatedsimultaneously.ThispropertyisimportantincomputingDarcyvelocitieso…     

INTERPOLATED FINITE ELEMENT METHODS FOR SECOND ORDER HYPERBOLIC EQUATIONS AND THEIR GLOBAL SUPERCONVERGENCE

We develop the interpolated finite element method to solve second-order hy-perbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation over adjacent elements. We prove that this interpo-lated finite element solution has superconvergence. This method can easily be applied togenerating more accurate gradient either locally or globally, depending on the applications.This method is also completely vectorizable and parallelizable to take the advantages ofmodern computer structures. Several numerical examples are presented to confirm ourtheoretical analysis.     

CHARACTERISTIC ALTERNATING-DIRECTION FINITE ELEMENT METHODS FOR NONRECTANGULAR REGIONS FOR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA AND ITS ANALYSIS

For coupled system of multilayer dynamics of fluids in porous media, the characteristic alternating-direction finite element methods for nourectangular regions applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, negative norm estimate, energy method, the theory of prior estimates and techniques are used. For the nourectangular regions case, optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved. These methods have been successfully used in multilayer oil resources migration-accumulation numerical simulation.     

EXTRAPOLATION FOR FINITE ELEMENT METHODS OF THE FIRST KIND FREDHOLM INTEGRAL EQUATIONS

In this paper,a numerical analysis of finite element methods for Fredholm equationsof the first kind,which is based upon regularization,is made.It shows that extrapolationalgorithms can accelerate the convergence of approximate solutions.     

HIGH-ACCURACY FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEM

1 IntroductionOptimal design or control is playing an increasingly importal role in engineering designwork. Efficient numerical methods are among the keys to successful application of optimalcontrol in practical work. With its wide range of application in scielltific and engineeringnumerical simulation, finite element approximation of optimal control problems plays a veryimportant role in numerical method of these problems. There have been eXtensive studies inthis respect, see, for example, […     

DEFECT CORRECTION FOR FINITE ELEMENT GRADIENT

A defect correction scheme of fourth order accuracy for linear finite element gradient is proposed in this note.This extends the Rannacher's scheme for finite element solution to gradient and can compete with superconvergence from quadratic elements.     

IMPLICIT—EXPLICIT MULTISTEP FINITE ELEMENT METHODS FOR THE SEMICONDUCTOR DEVICE PROBLEM

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by the finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The optimal L^2-norm error estimates are derived.     

HIGH ACCURACY ANALYSIS FOR FIRST ORDER HYPERBOLIC EQUATIONS BY PETROV-GALERKIN METHODS

1.IntroductionInthispaper,weareconcernedwiththefiniteelementmethodforthefollowingfirstorderhyperbolicequationwithsomeinitial--boundaryconditionwheref,gandvaresufficientlysmoothgivenfunctions.ItiswellknownthatthestandardGalerkinfiniteelementmethodisnotasvalidtothefirstorderhyperbolicproblemsasitistotheellipticandtheparabolicproblems.TheaccuracyofGalerkinll]solutionsfortheabetorderhyperbolicproblems,roughlyspeaking,losesoneorderwithrespecttotheaccuracyofthefiniteelemelltspaces.Moreover,Galerki…     

EIGENVALUE EXTRAPOLATION FORBIQUADRATIC FINITE ELEMENT APPROXIMATION IN RECTANGULAR DOMAIN

1.IntroductionItiswellknownthattheextrapolationmethodscanimprovetheaccuracyoffiniteelementsolutionandarewellstudiedinmanypapers.Wereferto[1--4]forafundamentalworkonasymptoticerrorexpansionsandextrapolationsandto[5]forasurveyonextrapolationtechniques.Forth…     

A posteriori error analysis of nonconforming methods for the eigenvalue problem

This paper extends the unifying theory for a posteriori error analysis of the nonconforming finite element methods to the second order elliptic eigenvalue problem. In particular, the author proposes the a posteriori error estimator for nonconforming methods of the eigenvalue problems and prove its reliability and efficiency based on two assumptions concerning both the weak continuity and the weak orthogonality of the nonconforming finite element spaces, respectively. In addition, the author examines these two assumptions for those nonconforming methods checked in literature for the Laplace, Stokes, and the linear elasticity problems.     

ACCURACY ANALYSIS OF 12-PARAMETER RECTANGULAR PLATE ELEMENTS WITH GEOMETRIC SYMMETRY

1. IntroductionAs for triangular thin plate element, it is observed in practice that the numerical accuxacyof the two unconventional plate elemellts, namely, the nine parameter quasi--conforming[1] andgeneralized conforming elements[2], is better than that of the usual Zienkiewicz's elemellt andSpecht's element[3], although all these elements have the same asymptotical rate of convergenceO(h) in the energy norm. How to explain the discrepancy between the theoretical analysis andnumerical comp…     

THE MODIFIED METHOD OF CHARACTERISTICS WITH FINITE ELEMENT OPERATOR—SPLITTING PROCEDURES FOR COMPRESSIBLE MULTICOMPONENT DISPLACEMENT PROBLEM

For the three-dimensional compressible multicomponent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting,characteristic method,calculus of variations,energy method,negative norm estimate,two kinds of test functions and the theory of prior estimates and techniques.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.These methods have been successfully used in oil-gas resources estimation,enhanced oil recovery simulation and seawater intrusion numerical simulation.     

FINITE ELEMENT ERROR EXPANSIONS FOR THE EIGENVALUE APPROXIMATION TO THE MULTIGROUP DIFFUSION EQUATIONS

Asymptotic expansions for the finite element approximation to the eigenvalues of the mult-igroup diffusion equations on Ω(?)R~n(n=2,3)of reactor theory are given,firstly for a piecewiseuniform triangulation,then for nonuniform quadrilateral meshes,and finally for nonuniformhexahedral meshes.The effect of certain classes of numerical integrations is studied.As applicationsof the expansions,several extrapolation formulas and a posteriori error estimates are obtained.     

AN EXTRAPOLATION METHODFOR FINITE ELEMENT APPROXIMATION OF INTEGRODIFFERENTIAL EQUATIONS WITH PARAMETERS

In this paper,we discuss the accelerating convergence method for finite elementapproximation of integro-differential equations with parameters.As applications,we give theerror estimates of finite element for the first kind of Fredholm integral equation,particularlyfor the Volterra integral equation with kernel condition k(x,x)=0.