Error Analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.

A RECOGNITION OF SIMPLE GROUPS PSL(3,q) BY THEIR ELEMENT ORDERS

For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

AN ADI GALERKIN METHOD WITH MOVING FINITE ELEMENT SPACES FOR A CLASS OF SECOND-ORDER HYPERBOLIC EQUATIONS

An alternating direction implicit (ADI) Galerkin method with moving finite element spaces is formulated for a class of second order hyperbolic equations in two space variables. A priori H 1 error estimate is derived.

The Confucian Scholar Class and the Establishment of Traditional Cultural Order

C ultural order is the inherent "soft"order,providing legal explanation and significant value system for the economic order and the political order. C ultural order means the rational,stable and orderly state in the cultural field,w hich can be divided into three levels: the value concept system of the ruling class,i. e.,the ideology of the state; the value system,attitude,belief and orientation of the populace; the self- conscious spirit and value concept system of the intellectual,w hich is represented by literature,art,philosophy and religion.T he establishment and maintenance of the cultural order asks for a group of people believing in such a culture and organizations,institutions and technology to guarantee it. Based on the possession of culture and know ledge and the combination of culture and authority,the C onfucian school class had their say in the traditional society,playing an important role in the establishment and maintenance of the traditional cultural order.

Evaluate All the Order of Every Element in the Higher Order of Group for Addition and Multiplication Composition

This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C× each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.

Finite Element Approach for the Solution of First-Order Differential Equations

The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differential equation into a system of algebraic equations by application of the method of weighted residuals in conjunction with a finite element ansatz. However, this procedure is restricted to even-ordered differential equations and leads to symmetric system matrices as a key property of the finite element method. This paper aims in a generalization of the finite element method towards the solution of first-order differential equations. This is achieved by an approach which replaces the first-order derivative by fractional powers of operators making use of the square root of a Sturm-Liouville operator. The resulting procedure incorporates a finite element formulation and leads to a symmetric but dense system matrix. Finally, the scheme is applied to the barometric equation where the results are compared with the analytical solution and other numerical approaches. It turns out that the resulting numerical scheme shows excellent convergence properties.

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before.

New Overview of the Energy Classification of Underlays

This article focuses on a new insight into the energy classification of sublayers. In this article, the study brings out very interesting and enriching information, knowledge and knowledge in atomistics. An affine function is represented in an orthonormal frame while assimilating a point to a sublayer. This made it possible to draw up a graph integrating each of the diagrams of the known energy levels. Our results are conclusive. We can then confirm that the research hypothesis is verified.

Numerical Simulation for Water Entry of a Wedge at Varying Speed by a High Order Boundary Element Method

一个高顺序边界元素方法为复杂速度潜力问题被开发。方法在每个元素而且速度的节点保证潜力的连续性不仅。它能被用于许多速度潜力问题。然而，现在的纸与改变速度集中了于它的应用程序到楔的水入口的问题。，当走方法的时间被使用时，此处完成的速度的连续性为这种非线性的免费表面流动问题是特别地重要的，免费表面通过在每个节点获得的速度被更新，速度的精确性因此是关键的。当，楔旅行了的距离 S 和时间 t 跟随关系 s=Dt 时，计算为一个盒子被做 D 并且是常数，它被发现导致自我类似流动地当效果由于严肃被忽略时。

The Counting Problem of an Order N-group of Set

In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.

Conjugate Class of Elements in A_6

The characterigation of A 6 is obtained through the method of calculation: The elements of A 6 is divided into seven conjugate classes.

Finite Element Analysis for the Structure Optimization Design of the CPUE Load-Bearing Wheel of Tracked Vehicle

A new kind of material cast polyurethane elastomers (CPUE) is introduced to take the place of rubber on load bearing wheel for the first time. Based on load bearing wheel dimensions, material properties and operating conditions, the structure of wheel flange is optimized by zero order finite element method. A detailed three dimensional finite element model of flange of load bearing wheel is developed and utilized to optimize structure of wheel flange. Its service life, which is affected by flange structure parameter, is analyzed by comparing the optimization results with those of prototype of wheel. The results of optimization are presented and the stress field of load bearing wheel in optimal dimension obtained by using finite element analysis method is demonstrated. The finite element analysis and optimization results show that the CPUE load bearing wheel is feasible and suitable for the tracked vehicle and has a guiding value in practice of the weighting design of the whole tracked vehicle.

Application of the quadrilateral area coordinate method:a new element for laminated composite plate bending problems

Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate （QAC） method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF （5-DOF per node） quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-rocessing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.

Numerical Experiments Using MATLAB: Superconvergence of Conforming Finite, Element Approximation for Second Order, Elliptic Problems

The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.

The Energy-orthogonal Tetrahedral Finite Element for Fourth Order Elliptic Equations

在这份报纸， 16 参数 nonconforming 有一个精力直角的形状函数空格的有四面的元素为第四份订单的 discretization 被介绍在三种空间尺寸的椭圆形的部分微分操作符。最新构造的元素被证明为一个模型 biharmonic 方程会聚。

A New Rectangular Finite Element Formulation Based on Higher Order Displacement Theory for Thick and Thin Composite and Sandwich Plates

A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains ( rxz and ryz) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.