线性定常对流占优对流扩散问题的有限体积——流线扩散有限元法

In this paper, two kinds of Finite Volume-Streamline Diffusion Finite Element methods (FV-SD) for steady convection dominated-diffusion problem are presented and the stability and error estimation for the numerical schemes considered are established in the norm stronger than L^2-norm. The theocratical analysis and numerical example show that the schemes constructed in this paper are keeping the basic properties of Streamline Diffusion (SD) method and they are more economical in computing scale than SD scheme, and also, they have same accuracy as FV-Galerkin FE method and better stability than it.     

一种新型的三维半解析数值算法

在三维空间,结合有限元线法与有限层法的思想,构造了一种新型的半解析数值算法,数值结果表明该方法具有较高的精度,切实可行。     

A term by term stabilization algorithm for finite element solution of incompressible flow problems

This paper introduces a stabilization technique for Finite Element numerical solution of 2D and 3D incompressible flow problems. It may be applied to stabilize the discretization of the pressure gradient, and also of any individual operator term such as the convection, curl or divergence operators, with specific levels of numerical diffusion for each one of them. Its computational complexity is reduced with respect to usual (residual-based) stabilization techniques. We consider piecewise affine Finite Elements, for which we obtain optimal error bounds for steady Navier-Stokes and also for generalized Stokes equations (including convection). We include some numerical experiment in well known 2D test cases, that show its good performances. Received March 15, 1996 / Revised version received January 17, 1997     

Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system

We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction of the electric permittivity function.     

Option pricing using multivariate Lévy processes

For d -dimensional Lévy models we provide a method for Finite Element-based asset pricing. We derive the partial integrodifferential pricing equation and prove that the corresponding variational problem is well-posed. Hereto, an explicit characterization of the domain of the bilinear form is given. For the numerical implementation the problem is discretized by sparse tensor product Finite Element spaces. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiple Impacts of Transversely Struck Aluminum Beams

Transverse impacts of steel spheres on aluminum beams are investigated numerically and experimentally. For the numerical investigation, modally-reduced models are used in combination with local Finite Element contact models. The proposed numerical models are verified by extensive experimental investigations using Laser-Doppler-Vibrometers. The numerical and experimental investigations show that impacts of steel spheres on aluminum beams yield strong structural vibrations causing multiple successive impacts. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Alternating Direction Methods for Hyperbolic Equations with Mixed Derivatives

Finite difference schemes for solving hyperbolic equations withvariable coefficients and mixed derivatives are collected together.A new alternating direction implicit algorithm is included.Splittings are suggested for this algorithm and numerical resultsare obtained.     

Finite element galerkin solutions for the strongly damped extensible beam equations

Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. The semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.     

ARTIFICIAL BOUNDARY METHOD FOR BURGERS'''' EQUATION USING NONLINEAR BOUNDARY CONDITIONS

This paper discusses the numerical solution of Burgers' equation on unbounded do-mains. Two artificial boundaries are introduced and boundary conditions are obtained onthe artificial boundaries, which are in nonlinear forms. Then the original problem is re-duced to an equivalent problem on a bounded domain. Finite difference method is appliedto the reduced problem, and some numerical examples are given to show the effectivenessof the new approach.     

Linear and nonlinear Finite Element modeling of coupled electro-magneto-mechanical multifield problems

In this paper we present the theoretical background and application of Finite Element algorithms for linear and nonlinear problems of multiple field coupling. They enable the prediction of the electromagnetomechanical behavior of materials and structures and supply useful tools for the optimization of multifunctional composites. First, linear three-field coupling is presented within the context of a Finite Element implementation. Then, a homogenization procedure is discussed. Finally, a micromechanical model for nonlinear ferroelectric constitutive behavior and its numerical realization are outlined. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

数值积分对完全非线性抛物型积分微分方程有限元方法的影响*

抛物型积分微分方程在带有记忆性的热传导 ,扩散 ,生物力学等实际问题中有广泛的应用 本文考虑如下模型 :ｃ(ｘ ,ｕ) ｔ = · {ａ(ｘ ,ｕ) ｕ + ∫ｔ0 ｂ(ｘ ,ｔ,τ ,ｕ(ｘ ,τ) ) ｕ(ｘ ,τ)ｄτ}+ ｆ(ｘ ,ｔ ,ｕ)　　　　　　　　　　　　　　　　 (ｘ ,ｔ) ∈Ω× [0 ,Ｔ]ｕ(ｘ ,ｔ) =0 ,　　 (ｘ ,ｔ)∈ Ω× [0 ,Ｔ]ｕ(ｘ ,0 ) =ｕ0 (ｘ) ,　　ｘ ∈Ω ,其中Ω Ｒｎ 为多角型区域 , Ω为边界 不用数值积分 ,对这类问题有限元方法研究已有很多工作[5 -8,11] ,导出了最优Ｌ2 及Ｈ1模估计 众所周知 ,解偏微分方程的有限元方法最终…     

一维多介质可压缩流动的守恒型界面追踪方法

本文针对一维问题的ProntTracking方法,提出了一种较易实现的守恒型界面追踪方法.利用双波近似求解Riemann问题来确定界面处的数值通量,在固定的网格上采用统一的有限体积格式进行内点和交界面点的计算,通过守恒插值以及守恒量的重新分配,保证数值解在全场实现一致守恒,将该方法应用于一维多介质可压缩流动的模拟,给出了满意的数值模拟结果.     

Hydrodynamical instability initiation in two-phase stratified flow using Spectral Method

In this article, the hydrodynamical instability initiation criterion in two-phase stratified flow in a horizontal duct is examined. The nonlinear two mass and two momentum conservation equations are used for numerical simulation using the two-phase two-fluid model. The model is solved using the Finite Volume and Spectral Methods, respectively. This paper is the first to utilize the Spectral Method for the simulation of two-phase flow problems. Using the Spectral Method, we show that the numerical error and CPU time decreases noticeably relative to the Finite Volume Method. The well established Kelvin–Helmholtz (K–H) instability is selected for the test case and comparison. The results taken from each set of computer codes developed in this paper are highly compatible with the theoretical and experimental results of previous researchers who used alternative numerical methods. The results obtained from the Spectral Method in comparison with the results of other well known codes exhibit greater consistency with prior analytical results, but with much smaller computer calculation time. The step taken in the present study shows a positive progress in two-phase two-fluid model numerical solution with hydrostatic assumption. It is recommended the research to be continued with two-phase two-fluid model but with hydrodynamical assumption.     

Effective viscous sintering parameters for heterogeneous plate-like structures using numerical homogenisation

A model to describe the sintering of plate-like structures and the numerical technique to obtain its ingredients from the analysis of a given heterogeneous structure are described. Finite membrane strains are accounted for and numerical creep tests are used to extract suitably defined macroscopic viscosities and generalised sintering stresses for plate-like structures. An example is analysed and compared to a full 3D simulation. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Augmented high order finite volume element method for elliptic PDEs in non-smooth domains: Convergence study

The accuracy of a finite element numerical approximation of the solution of a partial differential equation can be spoiled significantly by singularities. This phenomenon is especially critical for high order methods. In this paper, we show that, if the PDE is linear and the singular basis functions are homogeneous solutions of the PDE, the augmentation of the trial function space for the Finite Volume Element Method (FVEM) can be done significantly simpler than for the Finite Element Method. When the trial function space is augmented for the FVEM, all the entries in the matrix originating from the singular basis functions in the discrete form of the PDE are zero, and the singular basis functions only appear in the boundary conditions. That is to say, there is no need to integrate the singular basis functions over the elements and the sparsity of the matrix is preserved without special care. FVEM numerical convergence studies on two-dimensional triangular grids are presented using basis functions of arbitrary high order, confirming the same order of convergence for singular solutions as for smooth solutions.     

Finite difference approximation of a nonlinear integro-differential system

Finite difference approximation of the nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is studied. The convergence of the finite difference scheme is proved. The rate of convergence of the discrete scheme is given. The decay of the numerical solution is compared with the analytical results proven earlier.     

Finite dimensional cone iteration techniques for superlinear hammerstein equations 1

Finite dimensional iteration schemes are constructed which yield pointwise inclusions for unstable solutions of superlinear Hammerstein equations. The basic idea is to combine the method of cone iteration with a certain discretization technique. The method's high degree of accuracy is demonstrated by means of numerical examples.     

A comparison of numerical solutions of fractional diffusion models in finance

We compare the numerical solutions of three fractional partial differential equations that occur in finance. These fractional partial differential equations fall in the class of Lévy models. They are known as the FMLS (Finite Moment Log Stable), CGMY and KoBol models. Conditions for the convergence of each of these models is obtained.     

A higher order Finite Volume resolution method for a system related to the inviscid primitive equations in a complex domain

We construct the cell-centered Finite Volume discretization of the two-dimensional inviscid primitive equations in a domain with topography. To compute the numerical fluxes, the so-called Upwind Scheme (US) and the Central-Upwind Scheme (CUS) are introduced. For the time discretization, we use the classical fourth order Runge–Kutta method. We verify, with our numerical simulations, that the US (or CUS) is a robust first (or second) order scheme, regardless of the shape or size of the topography and without any mesh refinement near the topography.     

Estimation of the effect of numerical integration in finite element eigenvalue approximation

Summary Finite element approximations of the eigenpairs of differential operators are computed as eigenpairs of matrices whose elements involve integrals which must be evaluated by numerical integration. The effect of this numerical integration on the eigenvalue and eigenfunction error is estimated. Specifically, for 2nd order selfadjoint eigenvalue problems we show that finite element approximations with quadrature satisfy the well-known estimates for approximations without quadrature, provided the quadrature rules have appropriate degrees of precision.The work of this author was partially supported by the National Science Foundation under Grant DMS-84-10324