A modified Bakhvalov mesh

We consider a few numerical methods for solving a one-dimensional convection–diffusion singularly perturbed problem. More precisely, we introduce a modified Bakvalov mesh generated using some implicitly defined functions. Properties of this mesh and convergence results for several methods on it are given. Numerical results are presented in support of the theoretical considerations.     

随机平面弹性问题的协调有限元分析

This paper considers the numerical solution of plane elasticity equations with stochastic Young's modulus and stochastic loads.The stochastic fields are approximated by Karhunen-Loeve expansion and Wiener polynomial chaos expansion along sample paths,and in space continuous Lagrangian finite elements axe used.Error estimates are derived.Numerical experiments are done to verify the theoretical results.     

二次Lagrangian有限元方程的几何多重网格法

为了构造快速求解二次Lagrangian有限元方程的几何多重网格法,在选择二次Lagrangian有限元空间和一系列线性Lagrangian有限元空间分别作为最细网格层和其余粗网格层以及构造一种新限制算子的基础上,提出了一种新的几何多重网格法,并对它的计算量进行了估计.数值实验结果,与通常的几何多重网格法和AMG01法相比,表明了新算法计算量少且稳健性强.     

基于网格变动的油水驱动半正定问题迎风混合元方法

在网格随时间变动的有限元空间上研究了不可压缩的两相渗流驱动问题.分别对饱和度方程扩散矩阵正定和半正定的情形,提出了基于网格变动的迎风混合元方法混合元逼进压力方程,饱和度方程的对流项采用迎风格式来处理,扩散项则采用推广的混合元来逼进.在网格任意变动的情形下得到几乎最优的误差估计;对正定问题的格式进行改进,即在两个网格之间投影变化时采取近似解的线性构造,可以得到与固定网格时相同的最优收敛阶.     

Finite element modelling of surface waves in a channel

A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms.     

Boundary element method for calculation of effective elastic moduli in 3D linear elasticity

A boundary integral formulation of the linear elasticity problem for a multi‐component composite is given. The fast BEM solver based on the adaptive cross approximation is then obtained by the data‐sparse representation of the resulting Galerkin matrices. The solver is used to obtain effective elastic moduli of fibre and particle reinforced composites in three dimensions by means of the strain energy equivalence principle. Copyright © 2009 John Wiley & Sons, Ltd.     

A Petrov-Galerkin method for equal width equation

The equal width equation is solved numerically by Petrov-Galerkin method using linear hat function and quadratic B-spline function as trial and test functions respectively. Product approximation has been used in this method. A linear stability analysis of the scheme is shown to be conditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested method, which is found to be accurate and efficient. The Maxwellian initial condition pulse and the development of an undular bore are also studied.     

A boundary element method to price time-dependent double barrier options

In this paper we propose a new method for pricing double-barrier options with moving barriers under the Black-Scholes and the CEV models. First of all, by applying a variational technique typical of the boundary element method, we derive an integral representation of the double-barrier option price in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. Second, we develop an ad hoc numerical method to regularize and solve the system of integral equations obtained. Several numerical experiments are carried out showing that the overall algorithm is extraordinarily fast and accurate, even if the barriers are not differentiable functions. Moreover the numerical method presented in this paper performs significantly better than the finite difference approach.     

On Characterizations of Special Elements in Rings with Involution

Let $R$ be a ring with involution. It is well-known that an EPelement in $R$ is a core invertible element, but the question when acore invertible element is an EP element, the authors answer in thispaper. Several new characterizations of star-core, normal andHermitian elements in $R$ are also presented.     

A time-stepping procedure based on convolution for the mixed finite element approximation for porous media flow

A time-stepping procedure is established and analyzed for the problem of miscible displacement in porous medium. The fluid velocity based on mixed element method is post-processed by the convolution with Bramble-Schatz kernel. Convergence analysis shows that the property of superconvergence, originally held for the approximation of velocity, can be retained for the approximation of concentration variable. Compared with the traditional results in references, the constraint conditions between parameters in this paper are improved essentially.