Effect of numerical integration in the DGFEM for nonlinear convection‐diffusion problems

This paper is concerned with the effect of numerical integration applied to the discontinuous Galerkin finite element discretization of nonlinear convection‐diffusion problems in 2D. In the space semidiscretization the volume and line integrals are evaluated by numerical quadratures. Our goal is to estimate the error caused by the numerical integration and to show what numerical quadratures guarantee that the accuracy of the method with exact integration is preserved. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Superconvergence of finite volume element method for a nonlinear elliptic problem

In this article, we consider the finite volume element method for the second‐order nonlinear elliptic problem and obtain the H¹ and W^1,∞ superconvergence estimates between the solution of the finite volume element method and that of the finite element method, which reveal that the finite volume element method is in close relationship with the finite element method. With these superconvergence estimates, we establish the L^p and W^1,p (2 < p ≤ ∞) error estimates for the finite volume element method for the second‐order nonlinear elliptic problem. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Generating even triangulations of the projective plane

We shall determine the 20 families of irreducible even triangulations of the projective plane. Every even triangulation of the projective plane can be obtained from one of them by a sequence of even‐splittings and attaching octahedra, both of which were first given by Batagelj 2 . © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 333–349, 2007     

均匀自由流动的非牛顿流体中连续表面上的磁流体动力学流动和热传递

分析在平行自由流动的非牛顿黏弹性导电流体中,连续平展表面移动时的稳态流和热传递特性,该流动处于横向均匀磁场作用下.以二阶流体构建它的本构方程,得到了速度分布和温度断面图的数值结果.讨论了诸如黏弹性参数、磁场参数和Prandtl数等不同物理参数对诸种动量和热传递特性的影响,并给出相关图示.     

Metrizability and Coconnectedness

Solving the problem stated in Sichler and Trnková, Topol. Its Appl., 142: 159–179, 2004, we construct metrics μ, ν on a set P such that the spaces X=(P,μ) and Y=(P,ν) have the same monoid of all continuous selfmaps, the space Y is coconnected (in the sense that every continuous map Y×Y→Y depends on at most one coordinate) while X is not. Also, properties of the forgetful functors Metr → Unif → Top are investigated for the “simultaneous variant” of the above problem. Supported by the Grant Agency of Czech Republic under grant 201/06/0664 and by the project of Ministry of Education of Czech Republic MSM 0021620839.     

Edgeworth Expansions for Studentized Versions of Symmetric Finite Population Statistics

We show the validity of the one-term Edgeworth expansion for Studentized asymptotically linear statistics based on samples drawn without replacement from finite populations. Replacing the moments defining the expansion by their estimators, we obtain an empirical Edgeworth expansion. We show the validity of the empirical Edgeworth expansion in probability.     

A segregated method for compressible flow computation. Part II: general divariant compressible flows

Typically, segregated methods have been used for the computation of incompressible flows whereas coupled solvers, for compressible flows. Compared to coupled solvers, segregated methods present the advantage of computational savings in RAM memory and CPU time, although at the cost of an inferior robustness. However, previously published segregated algorithms for general compressible flows are known to present pitfalls, like convergence to wrong solutions, lack of robustness in the presence of strong discontinuities, such as normal and oblique shocks, and complicated boundary condition imposition. Therefore, in this paper a segregated method for non‐isothermal compressible flows is proposed that preserves the thermodynamic coupling and overcomes the criticisms of existing methods. Copyright © 2005 John Wiley & Sons, Ltd.     

CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve thecorresponding results of [1, 2, 4-9, 11-15].     

Finite element and implicit Runge–Kutta implementation of an acoustics–convection upstream resolution algorithm for the time‐dependent two‐dimensional Euler equations

The second of a two‐paper series, this paper details a solver for the characteristics‐bias system from the acoustics–convection upstream resolution algorithm for the Euler and Navier–Stokes equations. An integral formulation leads to several surface integrals that allow effective enforcement of boundary conditions. Also presented is a new multi‐dimensional procedure to enforce a pressure boundary condition at a subsonic outlet, a procedure that remains accurate and stable. A classical finite element Galerkin discretization of the integral formulation on any prescribed grid directly yields an optimal discretely conservative upstream approximation for the Euler and Navier–Stokes equations, an approximation that remains multi‐dimensional independently of the orientation of the reference axes and computational cells. The time‐dependent discrete equations are then integrated in time via an implicit Runge–Kutta procedure that in this paper is proven to remain absolutely non‐linearly stable for the spatially‐discrete Euler and Navier–Stokes equations and shown to converge rapidly to steady states, with maximum Courant number exceeding 100 for the linearized version. Even on relatively coarse grids, the acoustics–convection upstream resolution algorithm generates essentially non‐oscillatory solutions for subsonic, transonic and supersonic flows, encompassing oblique‐ and interacting‐shock fields that converge within 40 time steps and reflect reference exact solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

有源腔模式的有限元数值矩阵计算法

提出了一种计算有源腔模式分布的有限元数值矩阵方法。对腔镜进行基于菲涅耳–基尔霍夫衍射积分定理的有限元划分,利用MATLAB计算出光一次往返的传输矩阵。然后根据自再现理论,求出矩阵的特征值和特征向量。从而确定谐振腔的模式分布,给新型谐振腔的研究带来极大方便。