A Nonconforming Rectangular Finite Element Analysis for the Stokes Problem

A nonconforming rectangular finite element is presented, which satisfies the discrete B-B condition for the Stokes problem. And the element has two order convergence rate for the velocity and pressure.

Mixed Finite Element Formats of any Order Based on Bubble Functions for Stationary Stokes Problem

Mixed element formats of any order based on bubble functions for the stationary Stokes problem are derived in triangular and tetrahedral meshes and the convergence of these formats are proved.

Analysis on a Finite Volume Element Method for Stokes Problems

Finite volume element method for the Stokes problem is considered. We use a conforming piecewise linear function on a fine grid for velocity and piecewise constant element on a coarse grid for pressure. For general triangulation we prove the equivalence of the finite volume element method and a saddle-point problem, the inf-sup condition and the uniqueness of the approximation solution. We also give the optimal order H^1 norm error estimate. For two widely used dual meshes we give the L^2 norm error estimates, which is optimal in one case and quasi-optimal in another ease. Finally we give a numerical example.

CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

Two simplifled and stabilized mixed element formats for the Stokes problem are derived by bubble function, and their convergence, i.e., error analysis, are proved. These formats can save more freedom degrees than other usual formats.

A FICTITIOUS DOMAIN METHOD FOR DIRICHLET PROBLEM AND ITS APPLICATIONS TO GENER ALIZED STOKES PROBLEM

This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.

Test and Numerical Analysis on Performance of Reinforced Concrete Segment in Subway Tunnel

To investigate the mechanical behavior of segmental lining, a three-dimensional numerical analysis and test using three actual segments were used to analyze the effects of axial force and reinforcement ratio on the failure mechanism and ultimate bearing capacity of segmental lining. Both numerical and test results confirmed that the cracking load, yield and ultimate load were strongly influenced by axial force, and it was also proved that the yield and ultimate load would increase with the increase of reinforcement ratio, but the cracking load was almost not affected. The cracking load, yield and ultimate load are about 28.7%, 500% and 460% larger due to the effect of axial force respectively. The comparison between numerical calculation and test results showed that the finite element analysis resuits were in good agreement with the test results.

Stability evaluation of the Gümüshane-Akcakale cave by numerical analysis method

The Ak?akale Cave is located in the vicinity of the Arsa neighborhood within the boundaries of the Ak?akale village, Gümü?hane, Turkey. The cave is rich in cave formations(stalactite, stalagmite, cave pearl, cave flower, wall travertines). Thus, the appropriateness of opening the cave to visitors to boost tourism is of importance for the local and national economy. This study analyzes the stability of the Ak?akale Cave using a numerical analysis method. According to the results of the total displacement analysis, there are displacements in the entrance, ceiling, and sidewalls of the cave ranging from 1 mm to 48 mm. It seems that the entrance, ceiling, and sidewalls of the cave face a high risk of local or sudden collapse. According to the deformation analysis of the length section of the cave examined, local collapses may occur especially in the first 75 m from the entrance of the cave. We believe that this situation would not carry a risk for the Arsa neighborhood for now. In conclusion, the results of the stability analysis and in-situ observations showed clear evidence of former and ongoing cave-ins(collapses) and the Ak?akale Cave faces a high risk of local or sudden collapse. Thus, although the Ak?akale Cave is one of the most prominent karst caves in Turkey, it seems to be not appropriate to open the cave to tourist visits.

A Finite Volume Method Based on the Constrained Nonconforming Rotated Q_(1)-Constant Element for the Stokes Problem

We construct a finite volume element method based on the constrained nonconforming rotated Q_(1)-constant element(CNRQ_(1)-P_(0))for the Stokes problem.Two meshes are needed,which are the primal mesh and the dual mesh.We approximate the velocity by CNRQ_(1)elements and the pressure by piecewise constants.The errors for the velocity in the H^(1)norm and for the pressure in the L^(2)norm are O(h)and the error for the velocity in the L^(2)norm is O(h^(2)).Numerical experiments are presented to support our theoretical results.

TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.

CONVERGENCE OF A MIXED FINITE ELEMENT FOR THE STOKES PROBLEM ON ANISOTROPIC MESHES

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works .

ON THE APPROXIMATION OF INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEMS IN POROUS MEDIA BY MIXED AND STANDARD FINITE VOLUME ELEMENT METHODS

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations,the pressure–velocity equation and the concentration equation.In this paper,we present a mixed finite volume element method(FVEM)for the approximation of the pressure–velocity equation and a standard FVEM for the concentration equation.A priori error estimates in L^(∞)(L^(2))are derived for velocity,pressure and concentration.Numerical results are presented to substantiate the validity of the theoretical results.

Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface,where the arbitrary Lagrangian-Eulerian(ALE)technique is employed to deal with the moving and immersed subdomain.Stability and optimal convergence properties are obtained for both schemes.Numerical experiments are carried out for different scenarios of jump coefficients,and all theoretical results are validated.

THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

In this paper,we first propose a new stabilized finite element method for the Stokes eigenvalue problem.This new method is based on multiscale enrichment,and is derived from the Stokes eigenvalue problem itself.The convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also obtained.Moreover,we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue problem.Furthermore,we have proved a priori error estimates for this new two-level stabilized method.Finally,numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.

LOCALLY STABILIZED FINITE ELEMENT METHOD FOR STOKES PROBLEM WITH NONLINEAR SLIP BOUNDARY CONDITIONS

Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.

A PENALTY-HYBRID FINITE ELEMENT ANALYSIS OF STOKES FLOW

A type of penalty-hybrid variational principle is suggested for the analysis of Stokesian flow. On such a basis, a finite element model is formulated featuring, among others, a priori satisfaction of the deviatoric stress and hydrostatic pressure on linear momentum balance equations. Also in the present scheme the hydrostatic pressure is successfully eliminated at the element level, leaving only nodal velocities as solution unknowns. A series of 4-node and 8-node quadrilateral elements are derived and examined. Numerical examples demonstrating their characteristic behaviors are also included.

MIXED FINITE ELEMENT METHOD OF HEXAHEDRAL ELEMENTS FOR NAVIER-STOKES PROBLEM

In this paper, we derive a new mixed element format of hexahedral elements for Navier-Stokes problem in three-dimensional space.

A WEIGHTED PENALTY FINITE ELEMENT METHOD FOR THE ANALYSIS OF POWER-LAW FLUID FLOW PROBLEMS

In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.

Finite Element Analysis of 3-D Electromagnetic Field in Bloom Continuous Casting Mold

Three-dimensional finite element model of electromagnetic stirrer was built to predict magnetic field in a bloom continuous casting mold for steel during operation. The effects of current intensity, current frequency, and mold copper plate thickness on the magnetic field distribution in the mold were investigated. The results show that the magnetic induction intensity increases linearly with the increase in current intensity and decreases with the increase in current frequency. Increasing current intensity and frequency is available in increasing the electromagnetic force. The Joule heat decreases gradually from surface to center of bloom, and a maximum Joule heat can be found on corner of bloom. The prediction of magnetic induction intensity is in good agreement with the measured values.

Three-Dimensional Finite Element Numerical Simulation and Physical Experiment for Magnetism-Stress Detecting in Oil Casing

The casing damage has been a big problem in oilfield production. The current detection methods mostly are used after casing damage, which is not very effective. With the rapid development of China's offshore oil industry, the number of offshore oil wells is becoming larger and larger. Because the cost of offshore oil well is very high, the casing damage will cause huge economic losses. What's more, it can also bring serious pollution to marine environment. So the effective methods of detecting casing damage are required badly. The accumulation of stress is the main reason for the casing damage. Magnetic anisotropy technique based on counter magnetostriction effect can detect the stress of casing in real time and help us to find out the hidden dangers in time. It is essential for us to prevent the casing damage from occurring. However, such technique is still in the development stage. Previous studies mostly got the relationship between stress and magnetic signals by physical experiment, and the study of physical mechanism in relative magnetic permeability connecting the stress and magnetic signals is rarely reported. The present paper uses the ANSYS to do the three-dimensional finite element numerical simulation to study how the relative magnetic permeability works for the oil casing model. We find that the quantitative relationship between the stress' s variation and magnetic induction intensity's variation is: Δδ =K* ΔB, K = 8.04×109, which is proved correct by physical experiment.