电报方程的类Wilson非协调有限元分析

本文在矩形网格上讨论了半离散和全离散格式下电报方程的类Wilson非协调有限元逼近.利用该元在H1模意义下O(h2)阶的相容误差结果,平均值理论和关于时间t的导数转移技巧得到了超逼近性.进而,借助于插值后处理方法导出了超收敛结果.又由于该元在H1模意义下的相容误差可以达到O(h3)阶,构造了新的外推格式,给出了比传统误差估计高两阶的外推估计.最后,对于给出的全离散逼近格式得到了最优误差估计.     

对流扩散方程迎风有限元的自适应方法

本文对二维发展型对流扩散方程的迎风有限元格式给出了显式后验误差估计,证明了真实误差被后验误差估计器上下界定;并通过误差估计器建立了相应的自适应算法,数值例子表明了方法的有效性.     

特征值问题混合有限元法的一个误差估计

设（λh,σh,uh）是一个混合有限元特征对.Babuska和Osborn建立了（λh,uh）的误差估计.本文导出了σh的抽象误差估计式.并把该估计式应用于二阶椭圆特征值问题Raviart-Thomas混合有限元格式和重调和算子特征值问题Ciarlet-Raviart混合有限元格式,得到了一些新的误差估计.     

三维热传导型半导体问题的交替方向特征有限元方法

提出交替方向特征有限元方法,对电场位势方程采用混合元格式,对电子,空穴浓度方程采用交替方向特征有限元格式,对温度方程提出交替方向格式.应用向量积计算及先验估计理论和技巧,得到最佳的L2误差估计.     

Klein-Gordon-Zakharov方程初边值问题的Legendre谱方法

研究Klein-Gordon-Zakharov方程初边值问题的Legendre谱方法.在先验估计的基础上,证明了该格式的稳定性和收敛性,并得到最优阶误差估计.另外,还设计了一个半隐格式,并给出数值例子.在文章的后面给出了多区域谱格式,数值结果表明精度要高于单区域.     

非线性波动方程的各向异性有限元方法

研究了非线性波动方程的各向异性有限元方法,得到了半离散格式下的最优误差估计.     

正则长波方程的三次配点法

本文讨论了正则长波方程(RLW方程)的三次配点法,得到半离散格式的最优阶误差估计,同时给出基于向后Euler法的全离散格式,并证明了相应的误差估计.     

一维二阶椭圆型方程组的超收敛二次有限体积元方法

本文针对二阶椭圆型常微分方程组边值问题提出二次超收敛有限体积元方法,证明格式的H1和L2模误差估计,并给出应力佳点处的梯度超收敛估计.最后,编写计算格式的Fortran程序,用数值算例验证了理论分析的正确性和格式的有效性.     

热传导方程的间断Galerkin数值解法

本文对具有周期边界的热传导方程采用间断Galerkin(DG)方法给出数值求解方法,并利用傅里叶分析,对数值解进行L∞-误差估计,以一次分段多项式为例,得到半离散格式的误差估计.     

多层渗流方程组合系统的迎风分数步长差分方法和应用

对多层渗流方程组合系统提出适合并行计算的二阶和一阶两类迎风分数步长差分格式,利用变分形式、能量方法、二维和三维格式的配套、隐显格式的相互结合、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧,对二阶格式得到收敛性的最佳阶的L²误差估计. 对一阶格式亦得到收敛性的L²误差估计. 该方法已成功地应用到多层油资源运移聚集的评估生产实际中,得到了很好的数值模拟结果.     

平面弹性力学问题的混合元法的泡函数稳定性及其后验误差估计

该文讨论平面弹性力学问题的混合元法的泡函数稳定性,并导出基于简化的稳定化格式的一种先验误差估计和后验误差估计．这种简化的稳定化格式较通常的格式节省自由度．     

二阶椭圆问题基于泡函数的简化的稳定化二阶混合有限元格式

本文研究二阶椭圆方程基于泡函数的稳定化的二阶混合有限元格式,通过消去泡函数导出一种自由度很少的简化的稳定化的二阶混合有限元格式, 误差分析表明消去泡函数的简化格式与带有泡函数的格式具有相同的精度而可以节省6N_p个自由度(其中N_p三角形剖分中的顶点数目).       

On the connection between some linear triangular Reissner-Mindlin plate bending elements

Summary. We consider three triangular plate bending elements for the Reissner-Mindlin model. The elements are the MIN3 element of Tessler and Hughes [19], the stabilized MITC3 element of Brezzi, Fortin and Stenberg [5] and the T3BL element of Xu, Auricchio and Taylor [2, 17, 20]. We show that the bilinear forms of the stabilized MITC3 and MIN3 elements are equivalent and that their implementation may be simplified by using numerical integration of reduced order. The T3BL element is shown to be essentially the same as the MIN3 and stabilized MITC3 elements with reduced integration. We finally introduce a general stabilized finite element formulation which covers all three methods. For this class of methods we prove the stability and optimal convergence properties. Received November 4, 1996 / Revised version received May 29, 1997 / Published online January 27, 2000     

Stokes问题基于泡函数的简化的稳定化混合元格式的收敛性

利用泡函数导出Stokes问题的两种新的、简化的稳定化混合有限元格式.并证明这些格式与通常带泡函数的稳定化格式具有相同的收敛性,但是自由度可以大大减少.     

A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems

We propose a stabilized finite element method for the approximation of the biharmonic equation with a clamped boundary condition. The mixed formulation of the biharmonic equation is obtained by introducing the gradient of the solution and a Lagrange multiplier as new unknowns. Working with a pair of bases forming a biorthogonal system, we can easily eliminate the gradient of the solution and the Lagrange multiplier from the saddle point system leading to a positive definite formulation. Using a superconvergence property of a gradient recovery operator, we prove an optimal a priori estimate for the finite element discretization for a class of meshes.     

A parameter-free stabilized finite element method for scalar advection-diffusion problems

We formulate and study numerically a new, parameter-free stabilized finite element method for advection-diffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solving simplified one-dimensional versions of the governing equations on the edges. Then we use H(curl)-conforming edge elements to expand the resulting edge fluxes into an exponentially fitted flux field inside each element. Substitution of the nodal flux by this new flux completes the formulation of the method. Utilization of edge elements to define the numerical flux and the lack of stabilization parameters differentiate our approach from other stabilized methods. Numerical studies with representative advection-diffusion test problems confirm the excellent stability and robustness of the new method. In particular, the results show minimal overshoots and undershoots for both internal and boundary layers on uniform and non-uniform grids.     

A STABILIZED MIXED FINITE ELEMENT FORMULATION FOR THE NON-STATIONARY INCOMPRESSIBLE BOUSSINESQ EQUATIONS

In this study, we employ mixed finite element(MFE) method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence,uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.     

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.     

非定常Stokes方程的稳定化全离散有限体积元格式

本文研究非定常Stokes方程的有限体积元方法,给出一种基于两个局部高斯积分的稳定化全离散格式,并给其有限体积元解的误差分析.     

Finite volume method based on stabilized finite elements for the nonstationary Navier–Stokes problem

A finite volume method based on stabilized finite element for the two‐dimensional nonstationary Navier–Stokes equations is investigated in this work. As in stabilized finite element method, macroelement condition is introduced for constructing the local stabilized formulation of the nonstationary Navier–Stokes equations. Moreover, for P₁ ? P₀ element, the H¹ error estimate of optimal order for finite volume solution (u_h,p_h) is analyzed. And, a uniform H¹ error estimate of optimal order for finite volume solution (u_h, p_h) is also obtained if the uniqueness condition is satisfied. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007