关于“Bbble—隐定化有限元方法”的两点注记

本文针对Ｓｔｏｋｅｓ－问题给出了「１２」发展的基于局部ｂｕｂｂｌｅ－函数稳定化有限元与Ｇａｌｓ－稳定化有限元法，ｂｕｂｂｌｅ函数扩充元法的等价关系。     

Bubble—函数稳定化混合有限元分析

本文针对混合结构抽象问题，基于「９」的非标准稳定化有限元方法的一般框架研究了ｂｕｂｂｌｅ－函数稳定化方法，该逼近代格式使得Ｂａｂｕｓｋａ－Ｂｒｅｚｚｉ条件是不必要的。     

Stokes问题混合元方法中数值积分的影响

１引言用混合有限元方法求解Ｓｔｏｋｅｓ问题的近似解时,有两点重要事项．其一是众所周知的稳定化条件,这就导致在一阶及二阶格式中引人水泡（ｂｕｂｂｌｅ）函数（参见［１］,［２］,［４］和［６］）．其二是在实际计算中,含有体力密度ｆ的积分,需代之以数值积分,而保持原有的逼近阶不变．值得指出的是。该数值积分与水泡（ｂｕｂｂｌｅ）函数项无关．考虑数值积分下的Ｓｔｏｋｅｓ问题混合元逼近：设给定空间其中,是有界连通的多边形区域．考虑Ｓｔｏｋｅｓ问题混合变分形式：求Ｖ,ｐ　Ｍ,使得其中表示Ｌ２内积．众所周知,（…     

对流—扩散型问题Bubblc—稳定有限元分析

本文针地形如σｕ＋ａ．△↓ｕ－ｋ△ｕ＝ｆ对流－扩散型的模型问题，发展耦合局ｂｕｂｂｌｅ－函数的有限元方法，我们就ａ＝０和σ＝０两种情形证明了方法的与“影响因素”σ和Ｐｅｅｌｅｔ－数无关稳定生及全局最佳收敛阶。     

关于两个P-值逻辑函数的和函数的Chrestenson谱公式

类似于两个布尔函数的和函数的ｗａｌｓｈ谱公式,本文给出了两个３－值、５－值、７－值逻辑函数和函数的Ｃｈｒｅｓｔｅｎｓｏｎ谱公式。     

C-cosine算子函数的遍历性

在本文中,我们定义了 Ｃ－ｃｏｓｉｎｅ算子函数的 Ａｂｅｌ遍历性与Ｃｅｓàｒｏ遍历性,讨论了Ｃ－ｃｏｓｉｎｅ算子函数这两种遍历性的相互关系及基本性质,得到了其强Ａｂｅｌ遍历性在Ｒ（Ｃ）稠时的完全刻划．此外,我们还讨论了Ｃ－ｃｏｓｉｎｅ算子函数的轨道遍历性,并借助于Ｋ－泛函,给出了Ｃ－ｃｏｓｉｎｅ算子函数在０点以非最优化速率收敛的一个充要条件．     

关于Hurwitz zeta—函数的四次均值

对ｓ＝σ＋ｉｔ，ζ（ｓ，ａ）是Ｈｕｒｗｉｔｚｚｅｔａ－函数，ζ１（ｓ，ａ）＝ζ（ｓａ）－ａ＾－ｓ，。本文的主要目的是用解析的方法给出了Ｈｕｒｗｉｔｚｚｅｔａ－函数四次均值较强的渐近公式。     

F值函数的微分及其在FNN中的应用

本文引进了集值函数的ｓ－可微和模糊值（Ｆ值）函数的Ｆｓ－可微概念。给出了这两种可微性的几个判别条件。最后研究并得到了一类模糊神经网络（ＦＮＮ）的Ｆｓ－可微性和连续性。     

Banach函数空间上的Bessel(Riesz)位势及其应用(I)理论

本文首先引入Ｂｅｓｅｌ（Ｒｉｅｓｚ）位势Ｋ¨ｏｔｈｅ函数空间Ｘｓ（Ｘｓ）的概念，然后讨论一类算子在Ｌｅｂｅｓｇｕｅ－位势Ｋ¨ｏｔｈｅ函数空间Ｌｑ（－Ｔ，Ｔ；Ｘｓ）上的对偶估计．由此我们得到半群ｅｘｐ（ｉｔ（－Δ）ｍ／２）和算子Ａ：＝∫ｔ０ｅｘｐ（ｉ（ｔ－τ）（－Δ）ｍ／２）·ｄτ在Ｌｅｂｅｓｇｕｅ－Ｂｅｓｏｖ空间Ｌｑ－Ｔ，Ｔ；·Ｂｓｐ，２中的一些时间－－空间Ｌｐ－Ｌｐ′估计．本文的系列文将给出这些估计的应用     

RLW—Burgers方程的精确解

借助未知函数的变换，ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程化为易于求解的齐次形式的方程，从而得到ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程的精确解。     

稳定化有限元方法中逆估计常数的确定

0．弓I言稳定化有限元方法［2］［4］［12］［15］ro［18］在固体和流体力学的数值计算中构造有效的格式发挥着很大的作用．从理论分析的角度看，该方法（Galerkin一局部最小二乘方法）是完备的、确定的，但是在实际计算中稳定化参数。E（0，CI）的如何选取直接影响到逼近解的质量．数值实验【9川叫'川'到表明。取得太小会造成。伪l。压力模式rI．因此，对of的估计是一个值得注意的重要问题．文［8］虽然估训一了一些逆常数，但其未能给出确定逆估计常数的一般公式，而且技巧性太强，过于依赖区域剖分的性质，使得逆常数的计算复杂化，不…     

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).       

Analysis of the cell boundary element methods for convection dominated convection-diffusion equations

We introduce two kinds of the cell boundary element (CBE) methods for convection dominated convection-diffusion equations: one is the CBE method with the exact bubble function and the other with inexact bubble functions. The main focus of this paper is on inexact bubble CBE methods. For inexact bubble CBE methods we introduce a family of numerical methods depending on two parameters, one for control of interior layers and the other for outflow boundary layers. Stability and convergence analysis are provided and numerical tests for inexact bubble CBEs with various choices of parameters are presented.     

Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D

An adapted-bubbles approach which is a modification of the residual-free bubbles (RFB) method, is proposed for the Helmholtz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions. Unlike the other equations such as the advection-diffusion equation, RFB method when applied to the Helmholtz equation, does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems. Adapted-bubbles (AB) are obtained by a simple modification of the sub-problems. This modification increases the accuracy of the numerical solution impressively. We provide numerical experiments with the AB method up to $ch = 5$ where $c$ is the wavenumber and $h$ is the mesh size. Numerical tests show that the AB method is better by far than higher order methods available in the literature.     

底部加热肥皂泡上准二维湍流的数值模拟北大核心CSCD

底部加热的肥皂泡是一种全新的二维热对流模型,在实验中已发现肥皂泡上的岛涡运动规律与飓风轨迹规律一致.然而,肥皂泡的曲面特征对其准二维流场的数值模拟以及数据分析造成了较多困难.针对肥皂泡球面几何特征,该文介绍了其直接数值模拟(DNS)方法,及其流场空间波数谱、湍流通量和结构函数的计算分析方法.开展了Ra=3×10^(7),3×10^(9),3×10^(11)的数值计算,并获得了相应的波数谱、通量和湍流结构函数.计算结果表明,肥皂泡上速度的小尺度脉动特征满足Bo59的理论标度律,通过湍动能与拟涡能通量特征,发现在该准二维湍流场中存在湍流能量双级串现象.且随着Rayleigh数的增加,大尺度结构湍能量减小,更小尺度湍流结构能量增加.     

Finite element method solution of electrically driven magnetohydrodynamic flow

The magnetohydrodynamic (MHD) flow in a rectangular duct is investigated for the case when the flow is driven by the current produced by electrodes, placed one in each of the walls of the duct where the applied magnetic field is perpendicular. The flow is steady, laminar and the fluid is incompressible, viscous and electrically conducting. A stabilized finite element with the residual-free bubble (RFB) functions is used for solving the governing equations. The finite element method employing the RFB functions is capable of resolving high gradients near the layer regions without refining the mesh. Thus, it is possible to obtain solutions consistent with the physical configuration of the problem even for high values of the Hartmann number. Before employing the bubble functions in the global problem, we have to find them inside each element by means of a local problem. This is achieved by approximating the bubble functions by a nonstandard finite element method based on the local problem. Equivelocity and current lines are drawn to show the well-known behaviours of the MHD flow. Those are the boundary layer formation close to the insulated walls for increasing values of the Hartmann number and the layers emanating from the endpoints of the electrodes. The changes in direction and intensity with respect to the values of wall inductance are also depicted in terms of level curves for both the velocity and the induced magnetic field.     

Stabilized multiscale finite element method for the stationary Navier-Stokes equations

In the paper, a stabilized multiscale finite element method for the stationary incompressible Navier-Stokes equations is considered. The method is a Petrov-Galerkin approach based on the multiscale enrichment of the standard polynomial space enriched with the unusual bubble functions which no longer vanish on every element boundary for the velocity space. The stability of the P₁-P₀ triangular element (or the Q₁-P₀ quadrilateral element) is established. And the optimal error estimates of the stabilized multiscale finite element method for the stationary Navier-Stokes equations are obtained.     

A stabilized finite element method for convection–diffusion problems

A stabilized finite element method (FEM) is presented for solving the convection–diffusion equation. We enrich the linear finite element space with local functions chosen according to the guidelines of the residual‐free bubble (RFB) FEM. In our approach, the bubble part of the solution (the microscales) is approximated via an adequate choice of discontinuous bubbles allowing static condensation. This leads to a streamline‐diffusion FEM with an explicit formula for the stability parameter τ_K that incorporates the flow direction, has the capability to deal with problems where there is substantial variation of the Péclet number, and gives the same limit as the RFB method. The method produces the same a priori error estimates that are typically obtained with streamline‐upwind Petrov/Galerkin and RFB. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011     

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．