一种有限元亏量校正格式的误差估计

考虑边值问题及其有限元近似这里G是R”中有界域,a（。,v）二JZa。l＆。OI。＋ac。。是对称,比椭圆双线性形Gk,l＝1式,vkiEm。K）,凤。二裘Kl）一I入．x是定义在正规剖分几上的线性战Gn线性）有限元空间·用l＊11s;。表示Sobole。空间外,。（G）中范数,记11＊11s,。二l＊11s,加11。二扣名而．提高有限元解uh精度的一个基本工具是亏量校正．SO年代初期Frank等建立了一个亏量校正格式（见山）这里米是定义在TZ。上的二次（或n。次）有限元空间,Th是由马。中点加密得到的,他们有相同的节点．人是到光上的分片7次插值算子…     

两相渗流驱动问题的体积有限元数值计算和分析

本文在一般的三角形剖分上对两相渗流驱动提出了全离散体积有限元 ,并分析了带有弥散项时格式的收敛性 ,得到H1 模的最优估计 .     

位移障碍下四阶变分不等式问题的非协调有限元一般误差估计式

1.引 言 关于二阶变分不等式问题的非协调有限元逼近已有大量研究[1-5].但是,对于四阶变分不等式的研究相对而言较少[6-7].[8,9,10]给出了位移障碍问题的非协调有限元,包括C0元(如Zienkiewicz元及Adini元)和非C0元(如Morley元及De Veubeke元)逼近的理论分析及最优误差估计.经过仔细分析发现,其成功的关键技巧是充分利用上述单元的一个     

非线性双曲型方程的变网格有限元法

对一类非线性双曲型方程给出了两种变网格有限元逼近格式 .在一定条件下 ,得到了最优 H 1模误差估计     

A TWO-LEVEL FINITE ELEMENT GALERKIN METHOD FOR THE NONSTATIONARY NAVIER-STOKES EQUATIONS I： SPATIAL DISCRETIZATION

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.     

Numerical analysis of quenching – Heat conduction in metallic materials

Metallic materials present a complex behavior during heat treatment processes. In a certain temperature range, change of temperature induces a phase transformation of metallic structure, which alters physical properties of the material. Indeed, measurements of specific heat and conductivity show strong temperature-dependence during processes such as quenching of steel. Several mathematical models, as solid mixtures and thermal–mechanical coupling, for problems of heat conduction in metallic materials, have been proposed. In this work, we take a simpler approach without thermal–mechanical coupling of deformation, by considering the nonlinear temperature-dependence of thermal parameters as the sole effect due to those complex behaviors. The above discussion of phase transformation of metallic materials serves only as a motivation for the strong temperature-dependence as material properties. In general, thermal properties of materials do depend on the temperature, and the present formulation of heat conduction problem may be served as a mathematical model when the temperature-dependence of material parameters becomes important. For this mathematical model we present the error estimate using the finite element method for the continuous-time case.     

非定常Stokes方程的全离散稳定化有限元格式

本文研究二维非定常Stokes方程全离散稳定化有限元方法.首先给出关于时间向后一步Euler半离散格式,然后直接从该时间半离散格式出发,构造基于两局部高斯积分的稳定化全离散有限元格式,其中空间用P_1—P_1元逼近,证明有限元解的误差估计.本文的研究方法使得理论证明变得更加简便,也是处理非定常Stokes方程的一种新的途径.     

Numerical solutions of a two-phase membrane problem

In this paper different numerical methods for a two-phase free boundary problem are discussed. In the first method a novel iterative scheme for the two-phase membrane is considered. We study the regularization method and give an a posteriori error estimate which is needed for the implementation of the regularization method. Moreover, an efficient algorithm based on the finite element method is presented. It is shown that the sequence constructed by the algorithm is monotone and converges to the solution of the given free boundary problem. These methods can be applied for the one-phase obstacle problem as well.     

Optimal L ∞-Error Estimate of a Finite Element Method for Hamilton–Jacobi–Bellman Equations

This paper is concerned with the piecewise linear finite element approximation of Hamilton–Jacobi–Bellman equations. We establish the optimal L ^∞-error estimate, combining the concepts of subsolution and discrete regularity.     

THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS

1.IntroductionManyproblemsarisinginfluidmechanicsaregiveninanunboundeddomain,suchasfluidflowaroundobstacles.Whencomputingthenumericalsolutionsoftheseproblems,oneoftenintroducesartificialboundariesandsetsupaxtificialboundaryconditionsonthem.Thentheoriginal…     

CONVERGENCE OF AN ALTERNATING A-φ SCHEME FOR QUASI-MAGNETOSTATIC EDDY CURRENT PROBLEM

We propose in this paper an alternating A-$\phi$ method for the quasi-magnetostatic eddy current problem by means of finite element approximations. Bounds for continuous and discrete error in finite time are given. And it is verified that provided the time step $\tau$ is sufficiently small, the proposed algorithm yields for finite time $T$ an error of $O(h+\tau^{1/2})$ in the $L^2$-norm for the magnetic field $H(= \mu^{-1} \nabla \times A)$, where $h$ is the mesh size, $\mu$ the magnetic permeability.     

An enhanced finite volume method to model 2D linear elastic structures

This paper details the evaluation and enhancement of the vertex-centred finite volume method for the purpose of modelling linear elastic structures undergoing bending. A matrix-free edge-based finite volume procedure is discussed and compared with the traditional isoparametric finite element method via application to a number of test-cases. It is demonstrated that the standard finite volume approach exhibits similar disadvantages to the linear Q4 finite element formulation when modelling bending. An enhanced finite volume approach is proposed to circumvent this and a rigorous error analysis conducted. It is demonstrated that the developed finite volume method is superior to both standard finite volume and Q4 finite element methods, and provides a practical alternative to the analysis of bending-dominated solid mechanics problems.     

A new stabilized finite volume method for the stationary Stokes equations

In this paper we develop and study a new stabilized finite volume method for the two-dimensional Stokes equations. This method is based on a local Gauss integration technique and the conforming elements of the lowest-equal order pair (i.e., the P ₁–P ₁ pair). After a relationship between this method and a stabilized finite element method is established, an error estimate of optimal order in the H ¹-norm for velocity and an estimate in the L ²-norm for pressure are obtained. An optimal error estimate in the L ²-norm for the velocity is derived under an additional assumption on the body force. This work is supported in part by the NSF of China 10701001 and by the US National Science Foundation grant DMS-0609995 and CMG Chair Funds in Reservoir Simulation.     

Rate of weak convergence of the finite element method for the stochastic heat equation with additive noise

The stochastic heat equation driven by additive noise is discretized in the spatial variables by a standard finite element method. The weak convergence of the approximate solution is investigated and the rate of weak convergence is found to be twice that of strong convergence. M. Kovács and S. Larsson supported by the Swedish Research Council (VR). Part of this work was done at Institut Mittag-Leffler. S. Larsson supported by the Swedish Foundation for Strategic Research (SSF) through GMMC, the Gothenburg Mathematical Modelling Centre.     

Sobolev方程的全离散有限体积元格式及数值模拟

本文研究二维Sobolev方程的有限体积元方法, 给出一种全离散化有限体积元格式及其有限体积元解的误差估计,并用数值例子说明数值计算的结果与理论结果是相吻合的, 进一步说明了有限体积元方法比其他数值方法更优越.